具有Wentzell边界记忆阻尼的波动方程解的渐近行为  

Asymptotic Behavior of Solutions of Wave Equations with Wentzell Boundary Memory Damping

作　　者：任然 范小明[1] REN Ran;FAN Xiaoming(Department of Mathematics,Southwest Jiaotong University,Chengdu 611756,China)

机构地区：[1]西南交通大学数学学院,成都611756

出　　处：《重庆师范大学学报（自然科学版）》2021年第6期86-90,共5页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.71873111);重庆师范大学数学科学学院重点实验室项目。

摘　　要：【目的】研究带Wentzell边界且在该边界上具有记忆阻尼的线性波动方程解的能量衰减性质。【方法】由原方程变形构造出抽象的发展方程,使用线性算子的强连续半群理论。【结果】证明了该波动方程平衡解的强稳定性和非零解能量的收敛性。【结论】该波动方程的平衡解具有强稳定性,且任意非零解的能量随时间单调递减并收敛到0。[Purposes]The purpose is to investigate the energy decay of the solutions of linear wave equations with Wentzell boundary which has memory damping.[Methods]The abstract evolution equation is constructed from the original equation,and uses the theory of strong continuous semigroup of linear operators.[Findings]The strong stability of the equilibrium solution of the wave equation and the convergence of the energy of the non-zero solution are proved.[Conclusions]The equilibrium solution of the wave equation is strongly stable,and the energy of any nonzero solution of the wave equation monotonically converges to zero as the time goes to infinity.

关 键 词：Wentzell边界 波动方程 记忆阻尼 线性算子半群 强稳定性 

分 类 号：O193[理学—数学]