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

AIMS Mathematics

卷:6

Ahmed Himadan¹ 

[1] Department of Mathematics, College of Sciences and Arts, Qassim University, Ar-Rass, Saudi Arabia;

关键词: heat equation;    blow up;    weak-memory;    sobolev spaces;    variable exponents;   

DOI  :  10.3934/math.2021257

来源: DOAJ

【 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 place in consequence of a query to blow-up phenomenon.

【 授权许可】

Unknown