{"title":"由带漂移的退化波方程控制的、热传导条件下带记忆效应的传输系统的能量衰减率","authors":"Mohammad Akil, Genni Fragnelli, Ibtissam Issa","doi":"10.1002/mana.202300571","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we investigate the stabilization of the transmission problem of the degenerate wave equation and the heat equation under the Coleman–Gurtin heat conduction law or Gurtin–Pipkin law with the memory effect. We investigate the polynomial stability of this system when employing the Coleman–Gurtin heat conduction, establishing a decay rate of type <span></span><math>\n <semantics>\n <msup>\n <mi>t</mi>\n <mrow>\n <mo>−</mo>\n <mn>4</mn>\n </mrow>\n </msup>\n <annotation>$t^{-4}$</annotation>\n </semantics></math>. Next, we demonstrate exponential stability in the case when Gurtin–Pipkin heat conduction is applied.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The energy decay rate of a transmission system governed by the degenerate wave equation with drift and under heat conduction with the memory effect\",\"authors\":\"Mohammad Akil, Genni Fragnelli, Ibtissam Issa\",\"doi\":\"10.1002/mana.202300571\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper, we investigate the stabilization of the transmission problem of the degenerate wave equation and the heat equation under the Coleman–Gurtin heat conduction law or Gurtin–Pipkin law with the memory effect. We investigate the polynomial stability of this system when employing the Coleman–Gurtin heat conduction, establishing a decay rate of type <span></span><math>\\n <semantics>\\n <msup>\\n <mi>t</mi>\\n <mrow>\\n <mo>−</mo>\\n <mn>4</mn>\\n </mrow>\\n </msup>\\n <annotation>$t^{-4}$</annotation>\\n </semantics></math>. Next, we demonstrate exponential stability in the case when Gurtin–Pipkin heat conduction is applied.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-07-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/mana.202300571\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/mana.202300571","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The energy decay rate of a transmission system governed by the degenerate wave equation with drift and under heat conduction with the memory effect
In this paper, we investigate the stabilization of the transmission problem of the degenerate wave equation and the heat equation under the Coleman–Gurtin heat conduction law or Gurtin–Pipkin law with the memory effect. We investigate the polynomial stability of this system when employing the Coleman–Gurtin heat conduction, establishing a decay rate of type . Next, we demonstrate exponential stability in the case when Gurtin–Pipkin heat conduction is applied.
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