一类带有非线性边界耗散的粘弹性方程解的存在性和能量估计  

Existence of Solutions and Energy Estimates for a Viscoelastic Equation with Nonlinear Boundary Dissipation

作　　者：刘娟 蒲志林[1] LIU Juan;PU Zhilin(College of Mathematics and Software Science,Sichuan Normal University,Chengdu 610066,Sichuan)

机构地区：[1]四川师范大学数学与软件科学学院,四川成都610066

出　　处：《四川师范大学学报（自然科学版）》2018年第5期578-585,共8页Journal of Sichuan Normal University（Natural Science）

基　　金：四川省科技计划项目(2015JY0125)

摘　　要：主要研究带有非线性边界耗散的粘弹性方程解的存在唯一性和能量衰减估计.首先,采用FaedoGalerkin逼近方法证明全局解的存在唯一性并给出其变分形式;其次,利用积分不等式和索伯列夫迹嵌入定理得到方程解的能量衰减率.In this paper,we consider a viscoelastic equation with nonlinear boundary dissipation.We prove the existence and uniqueness of the solution by means of the Faedo-Galerkin method,and we obtain the explicit and general energy decay rate by making use of integral inequalities and Sobolev trace theorem.

关 键 词：非线性边界耗散 粘弹性方程 Faedo-Galerkin方法 能量衰减率 

分 类 号：O175.2[理学—数学]