EXISTENCE AND BLOW UP FOR A NONLINEAR VISCOELASTIC HYPERBOLIC PROBLEM WITH VARIABLE EXPONENTS

被引：3

作者：

Mahdi, Fatima Z. ^{[1
]}

Hakem, Ali ^{[1
]}

机构：

[1] Univ Djillali Liabes Sidi Bel Abbes, Lab ACEDP, POB 73, Sidi Bel Abbes 22000, Algeria

来源：

FACTA UNIVERSITATIS-SERIES MATHEMATICS AND INFORMATICS | 2020年 / 35卷 / 03期

关键词：

Variable exponents; weak solutions; blow up; WEAK SOLUTIONS; WAVE-EQUATION; DECAY; NONEXISTENCE; CONTINUITY; THEOREMS;

D O I：

10.22190/FUM12003647M

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Our aim in this paper is to establish the weak existence theorem and find under suitable assumptions sufficient conditions on m; p and the initial data for which the blow up takes place for the following boundary value problem: vertical bar u(t)vertical bar(rho) u(tt) - Delta u - Delta u(tt) + integral(t)(0) g(t - s) Delta u(s)ds + vertical bar u(t)vertical bar(m(x)-2) u(t) = vertical bar u vertical bar(p(x)-2)u. This paper extends some of the results obtained by the authors and it is focused on new results which are consequence of the presence of variable exponents.

引用

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页码：647 / 672

页数：26

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