Existence and uniqueness of solutions for a dynamic one-dimensional damage model

被引：50

作者：

Frémond, M ^{[1
]}

Kuttler, KL

Shillor, M

机构：

[1] CNRS, LCPC, Lab Mat & Struct Genie Civil, UMR 113, F-77420 Champs Marne, France

[2] Michigan Technol Univ, Dept Math Sci, Houghton, MI 49931 USA

[3] Oakland Univ, Dept Math & Stat, Rochester, MI 48309 USA

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 1999年 / 229卷 / 01期

关键词：

dynamic damage; damage under tension; viscoelastic rod; local existence and uniqueness; quenching;

D O I：

10.1006/jmaa.1998.6160

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a one-dimensional dynamic model that describes the evolution of damage caused by tension in a viscoelastic material. The process is modeled by a coupled set of two differential inclusions for the elastic displacement and damage fields. We establish the existence of local weak solutions. The existence result is derived from the a priori estimates obtained for a sequence of regularized, truncated, and time-retarded approximations. We also establish the existence of the unique weak solution of a simplified version of the model. (C) 1999 Academic Press.

引用

页码：271 / 294

页数：24

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