Well defined extinction time of solutions for a class of weak-viscoelastic parabolic equation with positive initial energy

被引：1

作者：

Himadan, Ahmed ^{[1
]}

机构：

[1] Qassim Univ, Coll Arts & Sci, Dept Math, Ar Rass, Saudi Arabia

来源：

AIMS MATHEMATICS | 2021年 / 6卷 / 05期

关键词：

heat equation; blow up; weak-memory; Sobolev spaces; variable exponents; EVOLUTION-EQUATIONS; WAVE-EQUATIONS; EXISTENCE; MULTIPLICITY; SYSTEM;

D O I：

10.3934/math.2021257

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the present paper, we consider an important problem from the point of view of application in sciences and mechanic, namely, a class of p(x)-Laplacian type parabolic equation with weak-viscoelasticity. Here, we are concerned with global in time non-existence under suitable conditions on the exponents q(x) and p(x) with positive initial energy. We show that the weak-memory term is unable to stabilize problem (1.2) under conditions (1.5) and (1.7). Our main interest in this paper arose in the first in of a to

引用

页码：4331 / 4344

页数：14

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