郑雅匀, 杨晗.一类非线性带延迟项粘弹性方程的初边值问题[J].重庆工商大学学报(自然科学版),2021,38(1):83-91
ZHENG Ya-yun,YANG Han.A Class of Initial Boundary Value Problems for Nonlinear Viscoelastic Equations with Delay Terms[J].Journal of Chongqing Technology and Business University(Natural Science Edition),2021,38(1):83-91
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
  
DOI:
中文关键词:  带延迟项粘弹性方程  Galerkin 方法  唯一性  整体弱解
英文关键词:viscoelastic equation with delay term  Galerkin method  uniqueness  global weak solution
基金项目:
作者单位
郑雅匀, 杨晗 西南交通大学 数学学院成都 611756 
摘要点击次数: 49
全文下载次数: 9
中文摘要:
      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。
英文摘要:
      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.
查看全文  查看/发表评论  下载PDF阅读器
关闭
重庆工商大学学报自然科学版 版权所有
地址:中国 重庆市 南岸区学府大道19号,重庆工商大学学报编辑部 邮编:400067
电话:023-62769495 传真:
您是第2348141位访客
关注微信二维码