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

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.