Global existence and nonexistence of solutions for a viscoelastic wave equation with nonlinear boundary source term

被引：11

作者：

Di, Huafei ^{[1
,2
]}

Shang, Yadong ^{[1
,2
]}

Peng, Xiaoming ^{[1
]}

机构：

[1] Guangzhou Univ, Sch Math & Informat Sci, Guangzhou 510006, Guangdong, Peoples R China

[2] Guangzhou Univ, Key Lab Math & Interdisciplinary Sci, Guangdong Higher Educ Inst, Guangzhou 510006, Guangdong, Peoples R China

来源：

MATHEMATISCHE NACHRICHTEN | 2016年 / 289卷 / 11-12期

关键词：

Viscoelastic equation; nonlinear boundary source; potential wells; invariant sets; POSITIVE-INITIAL-ENERGY; POTENTIAL WELL THEORY; BLOW-UP; UNIFORM DECAY; GENERAL DECAY; POSEDNESS;

D O I：

10.1002/mana.201500169

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider the initial boundary value problem for a viscoelastic wave equation with nonlinear boundary source term. First of all, we introduce a family of potential wells and prove the invariance of some sets. Then we establish the existence and nonexistence of global weak solution with small initial energy under suitable assumptions on the relaxation function g(.), nonlinear function f (.), the initial data and the parameters in the equation. Furthermore, we obtain the global existence of weak solution for the problem with critical initial conditions I(u(0)) >= 0 and E(0) = d. (C) 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

引用

页码：1408 / 1432

页数：25

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