Mathematics Subject Classification 1991

35-XX Partial differential equations ( 0 Dok.)

• 35-00 General reference works (handbooks, dictionaries, bibliographies, etc.) ( 0 Dok.)
• 35-01 Instructional exposition (textbooks, tutorial papers, etc.) ( 0 Dok.)
• 35-02 Research exposition (monographs, survey articles) ( 0 Dok.)
• 35-03 Historical (must be assigned at least one classification number from Section 01) ( 0 Dok.)
• 35-04 Explicit machine computation and programs (not the theory of computation or programming) ( 0 Dok.)
• 35-06 Proceedings, conferences, collections, etc. ( 0 Dok.)
• 35Axx General theory ( 0 Dok. )
• 35A05 General existence and uniqueness theorems ( 0 Dok.)
• 35A07 Local existence and uniqueness theorems, See also {35H05, 35Sxx} ( 0 Dok.)
• 35A08 Fundamental solutions ( 0 Dok.)
• 35A10 Cauchy-Kovalevskaya theorems ( 0 Dok.)
• 35A15 Variational methods ( 0 Dok.)
• 35A20 Analytic methods, singularities ( 0 Dok.)
• 35A22 Transform methods (e.g. integral transforms) ( 0 Dok.)
• 35A25 Other special methods ( 0 Dok.)
• 35A27 Microlocal methods; methods of sheaf theory and homological algebra in PDE, See also {32C38, 58G07} ( 0 Dok.)
• 35A30 Geometric theory, characteristics, transformations, See also {58G35, 58G37} ( 0 Dok.)
• 35A35 Theoretical approximation to solutions ( 0 Dok.)
• 35A40 Numerical approximation to solutions, {For numerical analysis, See 65Mxx, 65Nxx, 65P05} ( 0 Dok.)
• 35A99 None of the above but in this section ( 0 Dok.)
• 35Bxx Qualitative properties of solutions ( 0 Dok. )
• 35B05 General behavior of solutions of PDE (comparison theorems; oscillation, zeros and growth of solutions; mean value theorems) ( 0 Dok.)
• 35B10 Periodic solutions ( 0 Dok.)
• 35B15 Almost periodic solutions ( 0 Dok.)
• 35B20 Perturbations ( 0 Dok.)
• 35B25 Singular perturbations ( 0 Dok.)
• 35B27 Homogenization; partial differential equations in media with periodic structure, See also {73B27, 76D30} ( 0 Dok.)
• 35B30 Dependence of solutions of PDE on initial and boundary data, parameters, See also {58F14} ( 0 Dok.)
• 35B32 Bifurcation, See also {58F14} ( 0 Dok.)
• 35B35 Stability, boundedness ( 0 Dok.)
• 35B37 PDE in connection with control problems, See also {49J20, 49K20, 93C20} ( 0 Dok.)
• 35B40 Asymptotic behavior of solutions ( 0 Dok.)
• 35B45 A priori estimates ( 0 Dok.)
• 35B50 Maximum principles ( 0 Dok.)
• 35B60 Continuation and prolongation of solutions of PDE, See also {58A15, 58A17, 58Hxx} ( 0 Dok.)
• 35B65 Smoothness/regularity of solutions of PDE ( 0 Dok.)
• 35B99 None of the above but in this section ( 0 Dok.)
• 35Cxx Representations of solutions ( 0 Dok. )
• 35C05 Solutions in closed form ( 0 Dok.)
• 35C10 Series solutions, expansion theorems ( 0 Dok.)
• 35C15 Integral representations of solutions of PDE ( 0 Dok.)
• 35C20 Asymptotic expansions ( 0 Dok.)
• 35C99 None of the above but in this section ( 0 Dok.)
• 35Dxx Generalized solutions of partial differential equations ( 0 Dok. )
• 35D05 Existence of generalized solutions ( 0 Dok.)
• 35D10 Regularity of generalized solutions ( 0 Dok.)
• 35D99 None of the above but in this section ( 0 Dok.)
• 35Exx Equations and systems with constant coefficients, See Also { 35N05} ( 0 Dok. )
• 35E05 Fundamental solutions ( 0 Dok.)
• 35E10 Convexity properties ( 0 Dok.)
• 35E15 Initial value problems ( 0 Dok.)
• 35E20 General theory ( 0 Dok.)
• 35E99 None of the above but in this section ( 0 Dok.)
• 35Fxx General first-order equations and systems ( 0 Dok. )
• 35F05 General theory of linear first-order PDE ( 0 Dok.)
• 35F10 Initial value problems for linear first-order PDE, linear evolution equations ( 0 Dok.)
• 35F15 Boundary value problems for linear first-order PDE ( 0 Dok.)
• 35F20 General theory of nonlinear first-order PDE ( 0 Dok.)
• 35F25 Initial value problems for nonlinear first-order PDE, nonlinear evolution equations ( 0 Dok.)
• 35F30 Boundary value problems for nonlinear first-order PDE ( 0 Dok.)
• 35F99 None of the above but in this section ( 0 Dok.)
• 35Gxx General higher-order equations and systems ( 0 Dok. )
• 35G05 General theory of linear higher-order PDE ( 0 Dok.)
• 35G10 Initial value problems for linear higher-order PDE, linear evolution equations ( 0 Dok.)
• 35G15 Boundary value problems for linear higher-order PDE ( 0 Dok.)
• 35G20 General theory of nonlinear higher-order PDE ( 0 Dok.)
• 35G25 Initial value problems for nonlinear higher-order PDE, nonlinear evolution equations ( 0 Dok.)
• 35G30 Boundary value problems for nonlinear higher-order PDE ( 0 Dok.)
• 35G99 None of the above but in this section ( 0 Dok.)
• 35H05 Hypoelliptic equations and systems, See also {58Gxx} ( 0 Dok.)
• 35Jxx Partial differential equations of elliptic type, See also {{ 58Gxx} {58G05, 58G10}} ( 0 Dok. )
• 35J05 Laplace equation, reduced wave equation (Helmholtz), Poisson equation, See also {31Axx, 31Bxx} ( 0 Dok.)
• 35J10 Schrodinger operator, See also {35Pxx} ( 0 Dok.)
• 35J15 General theory of second-order, elliptic equations ( 0 Dok.)
• 35J20 Variational methods for second-order, elliptic equations ( 0 Dok.)
• 35J25 Boundary value problems for second-order, elliptic equations ( 0 Dok.)
• 35J30 General theory of higher-order, elliptic equations , See also {31A30, 31B30} ( 0 Dok.)
• 35J35 Variational methods for higher-order, elliptic equations ( 0 Dok.)
• 35J40 Boundary value problems for higher-order, elliptic equations ( 0 Dok.)
• 35J45 General theory of elliptic systems of PDE ( 0 Dok.)
• 35J50 Variational methods for elliptic systems ( 0 Dok.)
• 35J55 Boundary value problems for elliptic systems ( 0 Dok.)
• 35J60 Nonlinear PDE of elliptic type ( 0 Dok.)
• 35J65 Nonlinear boundary value problems for linear elliptic PDE; boundary value problems for nonlinear elliptic PDE ( 0 Dok.)
• 35J67 Boundary values of solutions to elliptic PDE ( 0 Dok.)
• 35J70 Elliptic partial differential equations of degenerate type ( 0 Dok.)
• 35J85 Unilateral problems and variational inequalities for elliptic PDE, See also {35R35, 49J40} ( 0 Dok.)
• 35J99 None of the above but in this section ( 0 Dok.)
• 35Kxx Parabolic equations and systems, See also {35Bxx, 35Dxx, 35R30, 35R35, 58G11} ( 0 Dok. )
• 35K05 Heat equation ( 0 Dok.)
• 35K10 General theory of second-order, parabolic equations ( 0 Dok.)
• 35K15 Initial value problems for second-order, parabolic equations ( 0 Dok.)
• 35K20 Boundary value problems for second-order, parabolic equations ( 0 Dok.)
• 35K22 Evolution equations (any order in the spatial derivatives), See also {58D25} ( 0 Dok.)
• 35K25 General theory of higher-order, parabolic equations ( 0 Dok.)
• 35K30 Initial value problems for higher-order, parabolic equations ( 0 Dok.)
• 35K35 Boundary value problems for higher-order, parabolic equations ( 0 Dok.)
• 35K40 General theory of parabolic systems of PDE ( 0 Dok.)
• 35K45 Initial value problems for pararabolic systems ( 0 Dok.)
• 35K50 Boundary value problems for parabolic systems ( 0 Dok.)
• 35K55 Nonlinear PDE of parabolic type ( 0 Dok.)
• 35K57 Reaction-diffusion equations ( 0 Dok.)
• 35K60 Nonlinear boundary value problems for linear parabolic PDE; boundary value problems for nonlinear parabolic PDE ( 0 Dok.)
• 35K65 Parabolic partial differential equations of degenerate type ( 0 Dok.)
• 35K70 Ultraparabolic, pseudoparabolic PDE, etc. ( 0 Dok.)
• 35K85 Unilateral problems and variational inequalities for parabolic PDE, See also {35R35, 49J40} ( 0 Dok.)
• 35K99 None of the above but in this section ( 0 Dok.)
• 35Lxx Partial differential equations of hyperbolic type, See Also { 58G16} ( 0 Dok. )
• 35L05 Wave equation ( 0 Dok.)
• 35L10 General theory of second-order, hyperbolic equations ( 0 Dok.)
• 35L15 Initial value problems for second-order, hyperbolic equations ( 0 Dok.)
• 35L20 Boundary value problems for second-order, hyperbolic equations ( 0 Dok.)
• 35L25 General theory of higher-order, hyperbolic equations ( 0 Dok.)
• 35L30 Initial value problems for higher-order, hyperbolic equations ( 0 Dok.)
• 35L35 Boundary value problems for higher-order, hyperbolic equations ( 0 Dok.)
• 35L40 General theory of hyperbolic systems of first-order PDE ( 0 Dok.)
• 35L45 Initial value problems for hyperbolic systems of first-order PDE ( 0 Dok.)
• 35L50 Boundary value problems for hyperbolic systems of first-order PDE ( 0 Dok.)
• 35L55 Hyperbolic systems of higher-order PDE ( 0 Dok.)
• 35L60 Nonlinear first-order PDE of hyperbolic type ( 0 Dok.)
• 35L65 Conservation laws ( 0 Dok.)
• 35L67 Shocks and singularities, See also {58C27, 76L05} ( 0 Dok.)
• 35L70 Nonlinear second-order PDE of hyperbolic type ( 0 Dok.)
• 35L75 Nonlinear hyperabolic PDE of higher ($gtr 2$) order ( 0 Dok.)
• 35L80 Hyperbolic PDE of degenerate type ( 0 Dok.)
• 35L85 Unilateral problems; variational inequalities for hyperbolic PDE, See also {35R35, 49J40} ( 0 Dok.)
• 35L99 None of the above but in this section ( 0 Dok.)
• 35Mxx Partial differential equations of special type (mixed, composite, etc.), {For degenerate types, See 35J70, 35K65, 35L80} ( 0 Dok. )
• 35M10 PDE of mixed type ( 0 Dok.)
• 35M20 PDE of composite type ( 0 Dok.)
• 35M99 None of the above but in this section ( 0 Dok.)
• 35Nxx Overdetermined systems, See also {{58Gxx} {58G05, 58G07, 58Hxx}} ( 0 Dok. )
• 35N05 Overdetermined systems with constant coefficients ( 0 Dok.)
• 35N10 Overdetermined systems with variable coefficients (general) ( 0 Dok.)
• 35N15 $overlinepartial$-Neumann problem and generalizations; formal complexes, See also {32F20 and 58G05} ( 0 Dok.)
• 35N99 None of the above but in this section ( 0 Dok.)
• 35Pxx Spectral theory and eigenvalue problems for partial differential operators, See also {47Axx, 47Bxx, 47F05} ( 0 Dok. )
• 35P05 General spectral theory of PDE ( 0 Dok.)
• 35P10 Completeness of eigenfunctions, eigenfunction expansions for PDO ( 0 Dok.)
• 35P15 Estimation of eigenvalues, upper and lower bounds ( 0 Dok.)
• 35P20 Asymptotic distribution of eigenvalues and eigenfunctions for PDO ( 0 Dok.)
• 35P25 Scattering theory for PDE, See also {47A40} ( 0 Dok.)
• 35P30 Nonlinear eigenvalue problems, nonlinear spectral theory for PDO ( 0 Dok.)
• 35P99 None of the above but in this section ( 0 Dok.)
• 35Qxx Equations of mathematical physics and other areas of application, See also {35J05, 35J10, 35K05, 35L05} ( 0 Dok. )
• 35Q05 Euler-Poisson-Darboux equation and generalizations ( 0 Dok.)
• 35Q15 Riemann-Hilbert problems, See also {30E25, 31A25, 31B20} ( 0 Dok.)
• 35Q30 Stokes and Navier-Stokes equations, See also {76D05, 76D07, 76N10} ( 0 Dok.)
• 35Q35 Other equations arising in fluid mechanics ( 0 Dok.)
• 35Q40 Equations from quantum mechanics ( 0 Dok.)
• 35Q51 Solitons, See also {58F07} ( 0 Dok.)
• 35Q53 KdV-like equations (Korteweg-de Vries, Burgers, sine-Gordon, sinh-Gordon, etc.), See also {58F07} ( 0 Dok.)
• 35Q55 NLS-like (nonlinear Schrodinger) equations, See Also { 58F07} ( 0 Dok.)
• 35Q58 Other completely integrable equations, See also {58F07} ( 0 Dok.)
• 35Q60 Equations of electromagnetic theory and optics ( 0 Dok.)
• 35Q72 Other equations from mechanics ( 0 Dok.)
• 35Q75 PDE in relativity ( 0 Dok.)
• 35Q80 Applications of PDE in areas other than physics ( 0 Dok.)
• 35Q99 None of the above but in this section ( 0 Dok.)
• 35Rxx Miscellaneous topics involving partial differential equations, {For equations on manifolds, See 58Gxx; for manifolds of solutions, See 58Bxx; for stochastic PDEs,See also 60H15} ( 0 Dok. )
• 35R05 PDE with discontinuous coefficients or data ( 0 Dok.)
• 35R10 Partial functional-differential or differential-difference equations, with or without deviating arguments ( 0 Dok.)
• 35R15 Partial differential equations on infinite-dimensional (e.g. function) spaces (= PDE in infinitely many variables), See also {46Gxx, 58D25} ( 0 Dok.)
• 35R20 Partial operator-differential equations (i.e. PDE on finite-dimensional spaces for abstract space valued functions), See also {34Gxx, 47A50, 47D03, 47D06, 47D09, 47H15, 47H20} ( 0 Dok.)
• 35R25 Improperly posed problems for PDE ( 0 Dok.)
• 35R30 Inverse problems (undetermined coefficients, etc.) for PDE ( 0 Dok.)
• 35R35 Free boundary problems for PDE ( 0 Dok.)
• 35R45 Partial differential inequalities ( 0 Dok.)
• 35R50 Partial differential equations of infinite order ( 0 Dok.)
• 35R60 Partial differential equations with randomness, See Also { 60H15} ( 0 Dok.)
• 35R70 PDE with multivalued right-hand sides ( 0 Dok.)
• 35R99 None of the above but in this section ( 0 Dok.)
• 35Sxx Pseudodifferential operators and other generalizations of partial differential operators, See also {47G30, 58G15} ( 0 Dok. )
• 35S05 General theory of $Psi$DO ( 0 Dok.)
• 35S10 Initial value problems for $Psi$DO ( 0 Dok.)
• 35S15 Boundary value problems for $Psi$DO ( 0 Dok.)
• 35S30 Fourier integral operators ( 0 Dok.)
• 35S35 Topological aspects: intersection cohomology, stratified sets, etc., See also {32C38, 32S40, 32S60, 58G07} ( 0 Dok.)
• 35S50 Paradifferential operators ( 0 Dok.)
• 35S99 None of the above but in this section ( 0 Dok.)