粘弹性材料中一类非线性方程组的整体经典解  

Global Classical Solutions for a Nonlinear Systems in Viscoelasticity

作　　者：刘法贵[1] 

机构地区：[1]华北水利水电学院数学系,郑州450011

出　　处：《数学年刊（A辑）》2008年第5期709-718,共10页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.10571024);河南省教育厅自然科学基金(No.2008A110011)资助的项目.

摘　　要：考虑具衰减记忆项的粘弹性材料中一类非线性方程组的Cauchy问题,在"大"初值条件下证明了经典解的整体存在性,给出了解在有限时间内产生奇性的充分条件,结果表明记忆具有耗散效应.The paper concerns with Cauchy problem for a nonlinear systems in viscoelasticity material with fading memory, and shows the existence of global calssical solutions to Cauehy problem with general ＇large＇ data, and gives a sufficient condition for developing singularities in the finite time. At the same time, for small fading memory, the author gives the estimates of life span of classical solution. It is shown that the memory effect produces the same result as the dissipation.

关 键 词：CAUCHY问题 粘弹性模型 经典解 

分 类 号：O175.27[理学—数学]