一类非线性带延迟项粘弹性方程的初边值问题  

A Class of Initial Boundary Value Problems for Nonlinear Viscoelastic Equations with Delay Terms

作　　者：郑雅匀 杨晗[1] ZHENG Ya-yun;YANG Han(School 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：《重庆工商大学学报（自然科学版）》2021年第1期83-91,共9页Journal of Chongqing Technology and Business University:Natural Science Edition

基　　金：国家自然科学基金项目资助(11701477).

摘　　要：粘弹性理论是固体力学的研究内容之一,粘弹性方程的初边值问题是近几年讨论热点话题之一,其中含有记忆项的粘弹性方程的研究成为微分方程中的重要课题;针对带有记忆项、时间延迟项的粘弹性方程的初边值问题研究,前人研究讨论的均为线性的阻力项,在此问题研究的基础上,提出了带有记忆项、时间延迟项和非线性阻力项的粘弹性方程的初边值问题;利用著名的Galerkin方法,通过构造近似解,对近似解进行先验估计并取极限,其中利用Cauchy-Schwarz不等式、Gronwall不等式、Young不等式等放缩得到了整体弱解的存在性,再通过提出假设并验证得到整体弱解的唯一性。Viscoelastic theory is one of the research contents of solid mechanics.The initial boundary value of the viscoelastic equation is one of the hot topics in recent years.The study of viscoelastic equations containing memory terms has become an important topic in differential equations.For the study of the initial boundary value of viscoelastic equations with memory term and time delay term,the previous researches discussed are linear resistance terms.Based on the research of this problem,the initial boundary value of the viscoelastic equation with memory term,time delay term and nonlinear damp term is proposed.Using the Galerkin method,by constructing an approximate solution,the prior solution of the approximate solution is estimated and the limit is taken.By using the enlargement and reduction of Cauchy-Schwarz inequality,Gronwall inequality and Young inequalies,the existence of the global weak solution is obtained.Then,the uniqueness of the global weak solution is obtained by putting forward hypotheses and verifying.

关 键 词：带延迟项粘弹性方程 GALERKIN方法 唯一性 整体弱解 

分 类 号：O175.2[理学—基础数学]