On the Existence of Viscosity Solutions for Evolution \( p(x) \)-Laplace Equation with One Spatial Variable

IF 0.58 Q3 Engineering

Journal of Applied and Industrial Mathematics Pub Date : 2025-07-11 DOI:10.1134/S1990478924040215

Ar. S. Tersenov

引用次数: 0

Abstract

In this paper, we study the first boundary value problem for the \( p(x) \)-Laplacian with one spatial variable in the presence of gradient terms that do not satisfy the Bernstein–Nagumo condition. A class of gradient nonlinearities is defined for which the existence of a viscosity solution that is Lipschitz continuous in \( x \) and Hölder continuous in \( t \) is proven.

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演化\( p(x) \) -单空间变量拉普拉斯方程黏度解的存在性

在不满足Bernstein-Nagumo条件的梯度项存在的情况下，研究了具有一个空间变量的\( p(x) \) -拉普拉斯算子的第一边值问题。定义了一类梯度非线性问题，证明了该类问题的粘性解在\( x \)中是Lipschitz连续的，在\( t \)中是Hölder连续的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Applied and Industrial Mathematics Engineering-Industrial and Manufacturing Engineering

CiteScore

1.00

自引率

0.00%

发文量

期刊介绍： Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.