带有记忆核的黏弹性方程解的能量衰减估计

Energy Decay Estimates of Solution for a Viscoelastic Equation with Memory Kernel

研究无界区域上带有记忆核的黏弹性方程解的能量衰减问题.证明当方程中的记忆函数满足一定条件时,系统的能量函数呈多项式衰减.证明过程主要依赖于构造合适的辅助函数以及一些积分不等式,结果推广了已有文献中的一些结果.

In this paper the energy decay estimate of solution for a viscoelastic equation with memory kernel in unbounded domain is investigated.It is proved that the energy function of system is polynomial decay when some conditions of the memory function of the equation are satisfied.The procedure of proof is completed by constructing appropriated auxiliary function and using integral inequalities.Besides,some results in previous literatures are generalized in this paper.