带有记忆项的多孔弹性方程解的衰减  

Decay of Solutions for Porous-elastic Equation with Memory Term

作　　者：刘瑶 李冬林 LIU Yao;LI Donglin(School of Mathematics Science,Shanxi University,Taiyuan 030006,China)

机构地区：[1]山西大学数学科学学院,山西太原030006

出　　处：《河南科技大学学报（自然科学版）》2020年第4期93-99,M0008,共8页Journal of Henan University of Science And Technology:Natural Science

基　　金：国家自然科学基金项目(11671240)。

摘　　要：研究了带有记忆项的多孔弹性方程在初始条件和第一类边界条件下解的衰减。通常一个记忆项足以使方程稳定,这与记忆项的核和方程的波速有关。本文证明了该方程解的一般衰减结果只与记忆项的核有关。在一些适当的假设下,用乘子法证明了方程解的一般衰减。The decay of solutions for the porous-elastic equation with memory term under initial condition and Dirichlet boundary condition was studied.In general,a memory term was enough to stabilize the equation,which was related to the kernel of the memory term and the wave speeds of the equation.It was proved that the general decay result of solutions for the equation was only related to the kernel of the memory term.Under some suitable assumptions,the general decay of solutions for the equation was proved by use of multiplier method.

关 键 词：多孔弹性方程 记忆项 一般衰减 松弛函数 LYAPUNOV函数 

分 类 号：O231.4[理学—运筹学与控制论]