Eduardo H. Gomes Tavares , Mauricio Barbosa da Silva , Jinyun Yuan
{"title":"Characterization results for a third-order evolution equation with memory and infinite history","authors":"Eduardo H. Gomes Tavares , Mauricio Barbosa da Silva , Jinyun Yuan","doi":"10.1016/j.jde.2025.113494","DOIUrl":null,"url":null,"abstract":"<div><div>The characterization of certain properties related to a third-order evolution equation with memory and infinite history will be discussed in this work. It is well-known that the existence and stability of solutions for equations of this nature depend on a relation between their parameters. By exploring classical tools from the semigroup theory of linear operators and working with a more general class of memory kernels, it will be proven here that such a relation is a sufficient and necessary condition for these properties.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"442 ","pages":"Article 113494"},"PeriodicalIF":2.4000,"publicationDate":"2025-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022039625005212","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
The characterization of certain properties related to a third-order evolution equation with memory and infinite history will be discussed in this work. It is well-known that the existence and stability of solutions for equations of this nature depend on a relation between their parameters. By exploring classical tools from the semigroup theory of linear operators and working with a more general class of memory kernels, it will be proven here that such a relation is a sufficient and necessary condition for these properties.
期刊介绍:
The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools.
Research Areas Include:
• Mathematical control theory
• Ordinary differential equations
• Partial differential equations
• Stochastic differential equations
• Topological dynamics
• Related topics