一类带有记忆核的黏弹性方程解的能量衰减估计

A Decay Result of the Energy to a Viscoelastic Equation with Memory Kernel

主要研究一类带有非退化记忆核的黏弹性系统解的能量衰减问题.弱化记忆函数g在已有文献中通常所需满足呈指数衰减的假设条件,并给出新的假设条件.证明当黏弹性方程中的记忆函数g满足新的假设条件时,随着时间趋于无穷,系统的能量函数呈指数衰减与多项式衰减只是特殊的衰减方式.研究结果推广了已有文献的一些结果.

In this paper,we study the fading behavior of energy for the solutions of a viscoelastic system with non-dissipative memory kernel.We give some new weaker assumptions on the memory function g,under which we obtain the result that the exponential and polynomial types of decay are only special cases.This work generalizes and improves the known results.