{"title":"具有时变记忆核的强阻尼波动方程的时变全局吸引子","authors":"Nguyen Duong Toan","doi":"10.1080/14689367.2022.2072710","DOIUrl":null,"url":null,"abstract":"In this paper, we consider the longtime behaviour for the strongly damped wave equation with time-dependent memory kernels on a bounded domain . The main novelty of our result is that the memory kernel depends on time, allowing to describe the dynamics of aging materials. We first investigate the existence and uniqueness of weak solutions and then, we obtain the existence of the time-dependent global attractors in . We also prove the regularity of the time-dependent global attractor , i.e. is bounded in , with a bound independent of t. Finally, when approaches a multiple of the Dirac mass at zero as , we prove that the asymptotic dynamics of our problem is close to the one of its formal limit describing viscoelastic solids of Kelvin–Voigt type.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":"37 1","pages":"466 - 492"},"PeriodicalIF":0.5000,"publicationDate":"2022-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Time-dependent global attractors for strongly damped wave equations with time-dependent memory kernels\",\"authors\":\"Nguyen Duong Toan\",\"doi\":\"10.1080/14689367.2022.2072710\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we consider the longtime behaviour for the strongly damped wave equation with time-dependent memory kernels on a bounded domain . The main novelty of our result is that the memory kernel depends on time, allowing to describe the dynamics of aging materials. We first investigate the existence and uniqueness of weak solutions and then, we obtain the existence of the time-dependent global attractors in . We also prove the regularity of the time-dependent global attractor , i.e. is bounded in , with a bound independent of t. Finally, when approaches a multiple of the Dirac mass at zero as , we prove that the asymptotic dynamics of our problem is close to the one of its formal limit describing viscoelastic solids of Kelvin–Voigt type.\",\"PeriodicalId\":50564,\"journal\":{\"name\":\"Dynamical Systems-An International Journal\",\"volume\":\"37 1\",\"pages\":\"466 - 492\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2022-05-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Dynamical Systems-An International Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1080/14689367.2022.2072710\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Dynamical Systems-An International Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/14689367.2022.2072710","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Time-dependent global attractors for strongly damped wave equations with time-dependent memory kernels
In this paper, we consider the longtime behaviour for the strongly damped wave equation with time-dependent memory kernels on a bounded domain . The main novelty of our result is that the memory kernel depends on time, allowing to describe the dynamics of aging materials. We first investigate the existence and uniqueness of weak solutions and then, we obtain the existence of the time-dependent global attractors in . We also prove the regularity of the time-dependent global attractor , i.e. is bounded in , with a bound independent of t. Finally, when approaches a multiple of the Dirac mass at zero as , we prove that the asymptotic dynamics of our problem is close to the one of its formal limit describing viscoelastic solids of Kelvin–Voigt type.
期刊介绍:
Dynamical Systems: An International Journal is a world-leading journal acting as a forum for communication across all branches of modern dynamical systems, and especially as a platform to facilitate interaction between theory and applications. This journal publishes high quality research articles in the theory and applications of dynamical systems, especially (but not exclusively) nonlinear systems. Advances in the following topics are addressed by the journal:
•Differential equations
•Bifurcation theory
•Hamiltonian and Lagrangian dynamics
•Hyperbolic dynamics
•Ergodic theory
•Topological and smooth dynamics
•Random dynamical systems
•Applications in technology, engineering and natural and life sciences