{"title":"Decay property for symmetric hyperbolic system with memory-type relaxation","authors":"N. Mori, Mari Okada, Shuichi Kawashima","doi":"10.1142/s0219530523500367","DOIUrl":null,"url":null,"abstract":"We consider the decay property for a symmetric hyperbolic system with memory-type relaxation. We assume that the memory kernel is a strongly positive definite kernel and prove that the system has the decay property of regularity-loss type. Our proof is based on a technical energy method in the Fourier space which makes use of the structural condition (called Craftsmanship condition or Condition (K)) and the modified properties of strongly positive definite kernels.","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":"13 3","pages":""},"PeriodicalIF":4.7000,"publicationDate":"2024-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s0219530523500367","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
引用次数: 0
Abstract
We consider the decay property for a symmetric hyperbolic system with memory-type relaxation. We assume that the memory kernel is a strongly positive definite kernel and prove that the system has the decay property of regularity-loss type. Our proof is based on a technical energy method in the Fourier space which makes use of the structural condition (called Craftsmanship condition or Condition (K)) and the modified properties of strongly positive definite kernels.
期刊介绍：
ACS Applied Bio Materials is an interdisciplinary journal publishing original research covering all aspects of biomaterials and biointerfaces including and beyond the traditional biosensing, biomedical and therapeutic applications.
The journal is devoted to reports of new and original experimental and theoretical research of an applied nature that integrates knowledge in the areas of materials, engineering, physics, bioscience, and chemistry into important bio applications. The journal is specifically interested in work that addresses the relationship between structure and function and assesses the stability and degradation of materials under relevant environmental and biological conditions.
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