带有非线性记忆的阻尼双曲方程组全局解的存在性与非存在性

Existence and Nonexistence of Global Solutions to a Damped Hyperbolic System with Nonlinear Memory

首先研究了带有非线性记忆的双曲方程组解的局部存在性.然后,在N=1的情况下,证明了小初值解的全局存在性,并给出了当t→∞时的渐近性态.最后在N≥1且初值是正的情况下,导出了全局解的非存在性结果.

The author studies the local existence of the solutions to a damped hyperbolic system with nonlinear memory. The global existence and the asymptotic behavior as t→∞ of solutions with small initial data are established in the case N = 1. Moreover, a nonexistence result of global solutions with some positive initial data is obtained for N ≥ 1.