{"title":"General decay for second-order abstract viscoelastic equation in Hilbert spaces with time delay","authors":"Houria Chellaoua, Y. Boukhatem","doi":"10.5269/bspm.52175","DOIUrl":null,"url":null,"abstract":"The paper is concerned with a second-order abstract viscoelastic equation with time delay and a relaxation function satisfying $ h^{\\prime}(t)\\leq -\\zeta(t) G(h(t))$. Under a suitable conditions, we establish an explicit and general decay rate results of the energy by introducing a suitable Lyaponov functional and some proprieties of the convex functions. Finally, some applications are given. This work generalizes the previous results without time delay term to those with delay.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":" ","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2022-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Boletim Sociedade Paranaense de Matematica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5269/bspm.52175","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
The paper is concerned with a second-order abstract viscoelastic equation with time delay and a relaxation function satisfying $ h^{\prime}(t)\leq -\zeta(t) G(h(t))$. Under a suitable conditions, we establish an explicit and general decay rate results of the energy by introducing a suitable Lyaponov functional and some proprieties of the convex functions. Finally, some applications are given. This work generalizes the previous results without time delay term to those with delay.