On Quasilinear Anisotropic Parabolic Equations with Time-Dependent Exponents

Al S. Tersenov; Ar S. Tersenov

doi:10.1134/S0037446620010140

On Quasilinear Anisotropic Parabolic Equations with Time-Dependent Exponents

Результат исследования: Научные публикации в периодических изданиях › статья › рецензирование

Аннотация

The Cauchy-Dirichlet problem for the anisotropic parabolic equation with variable exponents in the presence of a nonlinear source and gradient term is considered. We prove the existence and uniqueness of a weak solution that is Lipschitz continuous in the space variables.

Язык оригинала	английский
Страницы (с-по)	159-177
Число страниц	19
Журнал	Siberian Mathematical Journal
Том	61
Номер выпуска	1
DOI	https://doi.org/10.1134/S0037446620010140
Состояние	Опубликовано - янв 2020

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10.1134/S0037446620010140

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title = "On Quasilinear Anisotropic Parabolic Equations with Time-Dependent Exponents",

abstract = "The Cauchy-Dirichlet problem for the anisotropic parabolic equation with variable exponents in the presence of a nonlinear source and gradient term is considered. We prove the existence and uniqueness of a weak solution that is Lipschitz continuous in the space variables.",

keywords = "anisotropic parabolic equation, weak solution with bounded spatial derivatives, WEAK SOLUTIONS, EXISTENCE, UNIQUENESS, CONTINUITY, P(X",

author = "Tersenov, {Al S.} and Tersenov, {Ar S.}",

year = "2020",

month = jan,

doi = "10.1134/S0037446620010140",

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volume = "61",

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AU - Tersenov, Al S.

AU - Tersenov, Ar S.

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N2 - The Cauchy-Dirichlet problem for the anisotropic parabolic equation with variable exponents in the presence of a nonlinear source and gradient term is considered. We prove the existence and uniqueness of a weak solution that is Lipschitz continuous in the space variables.

AB - The Cauchy-Dirichlet problem for the anisotropic parabolic equation with variable exponents in the presence of a nonlinear source and gradient term is considered. We prove the existence and uniqueness of a weak solution that is Lipschitz continuous in the space variables.

KW - anisotropic parabolic equation

KW - weak solution with bounded spatial derivatives

KW - WEAK SOLUTIONS

KW - EXISTENCE

KW - UNIQUENESS

KW - CONTINUITY

KW - P(X

U2 - 10.1134/S0037446620010140

DO - 10.1134/S0037446620010140

M3 - Article

VL - 61

SP - 159

EP - 177

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 1

ER -

On Quasilinear Anisotropic Parabolic Equations with Time-Dependent Exponents

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