On the Existence of Viscosity Solutions of Anisotropic Parabolic Equations with Time-Dependent Anisotropy Exponents

被引：0

作者：

Tersenov A.S. ^{[1
]}

机构：

[1] Sobolev Institute of Mathematics, Siberian Branch, Russian Academy ofSciences, Novosibirsk

来源：

Journal of Applied and Industrial Mathematics | 2022年 / 16卷 / 04期

关键词：

anisotropic parabolic equation; time-dependent anisotropy exponent; viscosity solution;

D O I：

10.1134/S1990478922040214

中图分类号：

学科分类号：

摘要：

Abstract: We consider the Cauchy–Dirichlet problem for an anisotropic parabolic equation with agradient term that does not satisfy the Bernstein–Nagumo condition. The existence anduniqueness of a viscosity solution of this problem is proved. This solution is Höldercontinuous in time and Lipschitz continuous in the spatial variables. © 2022, Pleiades Publishing, Ltd.

引用

页码：821 / 833

页数：12

共 50 条

[41] SEMI-DISCRETIZATION IN TIME FOR PARABOLIC EQUATIONS WITH TIME-DEPENDENT OPERATOR
LEROUX, MN
RAIRO-ANALYSE NUMERIQUE-NUMERICAL ANALYSIS, 1979, 13 (02): : 119 - 137
[42] Long time behaviour of parabolic equations in time-dependent growing domains
Guesmia, Senoussi
Harkat, Soumia
ASYMPTOTIC ANALYSIS, 2018, 108 (04) : 187 - 219
[43] TIME-DEPENDENT SOLUTIONS OF MULTIMODE CONVECTION EQUATIONS
TOOMRE, J
GOUGH, DO
SPIEGEL, EA
JOURNAL OF FLUID MECHANICS, 1982, 125 (DEC) : 99 - 122
[44] EXISTENCE OF CONTINUOUS SOLUTIONS TO TIME-DEPENDENT VARIATIONAL INEQUALITIES
Barbagallo, Annamaria
JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 2006, 7 (03) : 343 - 353
[45] ON THE EXISTENCE AND UNIQUENESS OF SOLUTIONS TO TIME-DEPENDENT FRACTIONAL MFG
Cirant, Marco
Goffi, Alessandro
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2019, 51 (02) : 913 - 954
[46] EXISTENCE AND REPRESENTATION OF SOLUTIONS OF PARABOLIC EQUATIONS
EKLUND, NA
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1975, 47 (01) : 137 - 142
[47] EXISTENCE OF DISCONTINUOUS SOLUTIONS FOR PARABOLIC EQUATIONS
BLANC, P
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1990, 310 (02): : 53 - 56
[48] Time-dependent singularities in semilinear parabolic equations: Behavior at the singularities
Kan, Toni
Takahashi, Jin
JOURNAL OF DIFFERENTIAL EQUATIONS, 2016, 260 (10) : 7278 - 7319
[49] Localization of solutions of anisotropic parabolic equations
Antontsev, Stanislav
Shmarev, Sergey
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 71 (12) : E725 - E737
[50] The bounded slope condition for parabolic equations with time-dependent integrands
Schaetzler, Leah
Siltakoski, Jarkko
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2023, 30 (06):

← 1 2 3 4 5 →