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