35-XX 
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Partial differential equations
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35-00
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General reference works (handbooks, dictionaries, bibliographies, etc.)
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35-01
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Instructional exposition (textbooks, tutorial papers, etc.)
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35-02
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Research exposition (monographs, survey articles)
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35-03
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Historical {!must also be assigned at least one classification number from section 01}
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35-04
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Explicit machine computation and programs (not the theory of computation or programming)
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35-06
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Proceedings, conferences, collections, etc.
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35Axx
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General theory
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35A05
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General existence and uniqueness theorems
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35A07
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Local existence and uniqueness theorems
[See also
35H10 ,
35Sxx ]
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35A08
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Fundamental solutions
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35A10
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Cauchy-Kovalevskaya theorems
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35A15
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Variational methods
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35A17
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Parametrices
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35A18
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Wave front sets
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35A20
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Analytic methods, singularities
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35A21
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Propagation of singularities
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35A22
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Transform methods (e.g.
Integral transforms)
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35A25
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Other special methods
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35A27
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Microlocal methods; methods of sheaf theory and homological algebra in PDE
[See also
32C38 ,
58J15 ]
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35A30
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Geometric theory, characteristics, transformations
[See also
58J70 ,
58J72 ]
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35A35
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Theoretical approximation to solutions
{For numerical analysis, see
65Mxx ,
65Nxx }
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35A99
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None of the above, but in this section
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35Bxx
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Qualitative properties of solutions
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35B05
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General behavior of solutions of PDE (comparison theorems; oscillation, zeros and growth of solutions; mean value theorems)
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35B10
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Periodic solutions
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35B15
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Almost periodic solutions
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35B20
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Perturbations
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35B25
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Singular perturbations
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35B27
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Homogenization; partial differential equations in media with periodic structure
[See also
74Qxx ,
76M50 ]
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35B30
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Dependence of solutions of PDE on initial and boundary data, parameters
[See also
37Cxx ]
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35B32
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Bifurcation
[See also
37Gxx ,
37K50 ]
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35B33
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Critical exponents
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35B34
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Resonances
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35B35
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Stability, boundedness
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35B37
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PDE in connection with control problems
[See also
49J20 ,
49K20 ,
93C20 ]
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35B38
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Critical points
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35B40
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Asymptotic behavior of solutions
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35B41
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Attractors
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35B42
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Inertial manifolds
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35B45
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A priori estimates
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35B50
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Maximum principles
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35B60
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Continuation and prolongation of solutions of PDE
[See also
58A15 ,
58A17 ,
58Hxx ]
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35B65
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Smoothness and regularity of solutions of PDE
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35B99
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None of the above, but in this section
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35Cxx
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Representations of solutions
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35C05
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Solutions in closed form
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35C10
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Series solutions, expansion theorems
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35C15
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Integral representations of solutions of PDE
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35C20
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Asymptotic expansions
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35C99
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None of the above, but in this section
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35Dxx
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Generalized solutions of partial differential equations
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35D05
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Existence of generalized solutions
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35D10
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Regularity of generalized solutions
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35D99
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None of the above, but in this section
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35Exx
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Equations and systems with constant coefficients
[See also
35N05 ]
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35E05
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Fundamental solutions
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35E10
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Convexity properties
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35E15
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Initial value problems
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35E20
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General theory
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35E99
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None of the above, but in this section
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35Fxx
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General first-order equations and systems
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35F05
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General theory of linear first-order PDE
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35F10
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Initial value problems for linear first-order PDE, linear evolution equations
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35F15
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Boundary value problems for linear first-order PDE
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35F20
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General theory of nonlinear first-order PDE
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35F25
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Initial value problems for nonlinear first-order PDE, nonlinear evolution equations
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35F30
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Boundary value problems for nonlinear first-order PDE
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35F99
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None of the above, but in this section
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35Gxx
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General higher-order equations and systems
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35G05
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General theory of linear higher-order PDE
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35G10
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Initial value problems for linear higher-order PDE, linear evolution equations
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35G15
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Boundary value problems for linear higher-order PDE
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35G20
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General theory of nonlinear higher-order PDE
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35G25
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Initial value problems for nonlinear higher-order PDE, nonlinear evolution equations
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35G30
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Boundary value problems for nonlinear higher-order PDE
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35G99
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None of the above, but in this section
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35Hxx
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Close-to-elliptic equations
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35H10
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Hypoelliptic equations
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35H20
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Subelliptic equations
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35H30
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Quasi-elliptic equations
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35H99
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None of the above, but in this section
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35Jxx
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Partial differential equations of elliptic type
[See also
58Jxx ,
58J10 ,
58J20 ]
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35J05
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Laplace equation, reduced wave equation (Helmholtz), Poisson equation
[See also
31Axx ,
31Bxx ]
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35J10
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Schr\"odinger operator
[See also
35Pxx ]
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35J15
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General theory of second-order, elliptic equations
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35J20
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Variational methods for second-order, elliptic equations
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35J25
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Boundary value problems for second-order, elliptic equations
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35J30
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General theory of higher-order, elliptic equations
[See also
31A30 ,
31B30 ]
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35J35
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Variational methods for higher-order, elliptic equations
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35J40
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Boundary value problems for higher-order, elliptic equations
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35J45
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General theory of elliptic systems of PDE
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35J50
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Variational methods for elliptic systems
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35J55
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Boundary value problems for elliptic systems
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35J60
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Nonlinear PDE of elliptic type
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35J65
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Nonlinear boundary value problems for linear elliptic PDE; boundary value problems for nonlinear elliptic PDE
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35J67
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Boundary values of solutions to elliptic PDE
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35J70
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Elliptic partial differential equations of degenerate type
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35J85
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Unilateral problems and variational inequalities for elliptic PDE
[See also
35R35 ,
49J40 ]
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35J99
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None of the above, but in this section
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35Kxx
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Parabolic equations and systems
[See also
35Bxx ,
35Dxx ,
35R30 ,
35R35 ,
58J35 ]
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35K05
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Heat equation
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35K10
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General theory of second-order, parabolic equations
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35K15
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Initial value problems for second-order, parabolic equations
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35K20
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Boundary value problems for second-order, parabolic equations
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35K25
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General theory of higher-order, parabolic equations
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35K30
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Initial value problems for higher-order, parabolic equations
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35K35
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Boundary value problems for higher-order, parabolic equations
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35K40
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General theory of parabolic systems of PDE
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35K45
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Initial value problems for parabolic systems
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35K50
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Boundary value problems for parabolic systems
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35K55
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Nonlinear PDE of parabolic type
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35K57
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Reaction-diffusion equations
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35K60
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Nonlinear boundary value problems for linear parabolic PDE; boundary value problems for nonlinear parabolic PDE
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35K65
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Parabolic partial differential equations of degenerate type
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35K70
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Ultraparabolic, pseudoparabolic PDE, etc.
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35K85
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Unilateral problems and variational inequalities for parabolic PDE
[See also
35R35 ,
49J40 ]
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35K90
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Abstract parabolic evolution equations
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35K99
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None of the above, but in this section
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35Lxx
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Partial differential equations of hyperbolic type
[See also
58J45 ]
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35L05
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Wave equation
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35L10
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General theory of second-order, hyperbolic equations
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35L15
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Initial value problems for second-order, hyperbolic equations
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35L20
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Boundary value problems for second-order, hyperbolic equations
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35L25
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General theory of higher-order, hyperbolic equations
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35L30
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Initial value problems for higher-order, hyperbolic equations
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35L35
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Boundary value problems for higher-order, hyperbolic equations
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35L40
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General theory of hyperbolic systems of first-order PDE
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35L45
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Initial value problems for hyperbolic systems of first-order PDE
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35L50
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Boundary value problems for hyperbolic systems of first-order PDE
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35L55
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Hyperbolic systems of higher-order PDE
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35L60
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Nonlinear first-order PDE of hyperbolic type
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35L65
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Conservation laws
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35L67
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Shocks and singularities
[See also
58Kxx ,
76L05 ]
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35L70
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Nonlinear second-order PDE of hyperbolic type
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35L75
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Nonlinear hyperabolic PDE of higher ($\gtr 2$) order
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35L80
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Hyperbolic PDE of degenerate type
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35L82
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Pseudohyperbolic equations
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35L85
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Unilateral problems; variational inequalities forhyperbolic PDE
[See also
35R35 ,
49J40 ]
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35L90
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Abstract hyperbolic evolution equations
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35L99
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None of the above, but in this section
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35Mxx
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Partial differential equations of special type (mixed, composite, etc.)
{For degenerate types, see
35J70 ,
35K65 ,
35L80 }
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35M10
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PDE of mixed type
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35M20
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PDE of composite type
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35M99
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None of the above, but in this section
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35Nxx
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Overdetermined systems
[See also
58Jxx ,
58J10 ,
58J15 ,
58Hxx ]
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35N05
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Overdetermined systems with constant coefficients
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35N10
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Overdetermined systems with variable coefficients (general)
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35N15
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$\Overline\partial$-Neumann problem and generalizations; formal complexes
[See also
32W05 ,
32W10 ,
58J10 ]
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35N99
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None of the above, but in this section
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35Pxx
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Spectral theory and eigenvalue problems for partial differential operators
[See also
47Axx ,
47Bxx ,
47F05 ]
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35P05
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General spectral theory of PDE
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35P10
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Completeness of eigenfunctions, eigenfunction expansions for PDO
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35P15
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Estimation of eigenvalues, upper and lower bounds
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35P20
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Asymptotic distribution of eigenvalues and eigenfunctions for PDO
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35P25
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Scattering theory for PDE
[See also
47A40 ]
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35P30
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Nonlinear eigenvalue problems, nonlinear spectral theory for PDO
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35P99
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None of the above, but in this section
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35Qxx
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Equations of mathematical physics and other areas of application
[See also
35J05 ,
35J10 ,
35K05 ,
35L05 ]
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35Q05
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Euler-Poisson-Darboux equation and generalizations
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35Q15
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Riemann-Hilbert problems
[See also
30E25 ,
31A25 ,
31B20 ]
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35Q30
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Stokes and Navier-Stokes equations
[See also
76D05 ,
76D07 ,
76N10 ]
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35Q35
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Other equations arising in fluid mechanics
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35Q40
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Equations from quantum mechanics
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35Q51
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Solitons
[See also
37K40 ]
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35Q53
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KdV-like equations (Korteweg-de_Vries, Burgers, sine-Gordon, sinh-Gordon, etc.)
[See also
37K10 ]
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35Q55
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NLS-like (nonlinear Schr\"odinger) equations
[See also
37K10 ]
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35Q58
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Other completely integrable equations
[See also
37J35 ,
37K10 ]
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35Q60
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Equations of electromagnetic theory and optics
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35Q72
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Other equations from mechanics
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35Q75
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PDE in relativity
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35Q80
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Applications of PDE in areas other than physics
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35Q99
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None of the above, but in this section
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35Rxx
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Miscellaneous topics involving partial differential equations
{For equations on manifolds, see
58Jxx ;
for manifolds of solutions, see
58Bxx ;
for stochastic PDEs, see also
60H15 }
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35R05
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PDE with discontinuous coefficients or data
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35R10
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Partial functional-differential or differential-difference equations, with or without deviating arguments
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35R12
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Impulsive partial differential equations
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35R15
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Partial differential equations on infinite-dimensional (e.g.
Function) spaces (=PDE in infinitely many variables)
[See also
46Gxx ,
58D25 ]
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35R20
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Partial operator-differential equations (i.e. PDE on finite-dimensional spaces for abstract space valued functions)
[See also
34Gxx ,
47A50 ,
47D03 ,
47D06 ,
47D09 ,
47H20 ,
47Jxx ]
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35R25
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Improperly posed problems for PDE
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35R30
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Inverse problems (undetermined coefficients, etc.) for PDE
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35R35
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Free boundary problems for PDE
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35R45
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Partial differential inequalities
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35R50
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Partial differential equations of infinite order
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35R60
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Partial differential equations with randomness
[See also
60H15 ]
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35R70
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PDE with multivalued right-hand sides
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35R99
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None of the above, but in this section
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35Sxx
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Pseudodifferential operators and other generalizations of partial differential operators
[See also
47G30 ,
58J40 ]
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35S05
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General theory of PsDO
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35S10
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Initial value problems for PsDO
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35S15
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Boundary value problems for PsDO
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35S30
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Fourier integral operators
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35S35
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Topological aspects: intersection cohomology, stratified sets, etc.
[See also
32C38 ,
32S40 ,
32S60 ,
58J15 ]
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35S50
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Paradifferential operators
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35S99
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None of the above, but in this section
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