一类具有非线性记忆的自由边界问题的爆破与渐近性质

Pub Date : 2020-06-01 DOI:10.4208/jpde.v33.n3.5

Jiahui Huang

{"title":"一类具有非线性记忆的自由边界问题的爆破与渐近性质","authors":"Jiahui Huang","doi":"10.4208/jpde.v33.n3.5","DOIUrl":null,"url":null,"abstract":"In this paper, we investigate a reaction-diffusion equation ut−duxx = au+ ∫ t 0 u p(x,τ)dτ+k(x) with double free boundaries. We study blowup phenomena in finite time and asymptotic behavior of time-global solutions. Our results show if ∫ h0 −h0 k(x)ψ1dx is large enough, then the blowup occurs. Meanwhile we also prove when T∗<+∞, the solution must blow up in finite time. On the other hand, we prove that the solution decays at an exponential rate and the two free boundaries converge to a finite limit provided the initial datum is small sufficiently. AMS Subject Classifications: 35K20, 35R35, 92B05 Chinese Library Classifications: O175","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Blowup and Asymptotic Behavior of a Free Boundary Problem with a Nonlinear Memory\",\"authors\":\"Jiahui Huang\",\"doi\":\"10.4208/jpde.v33.n3.5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we investigate a reaction-diffusion equation ut−duxx = au+ ∫ t 0 u p(x,τ)dτ+k(x) with double free boundaries. We study blowup phenomena in finite time and asymptotic behavior of time-global solutions. Our results show if ∫ h0 −h0 k(x)ψ1dx is large enough, then the blowup occurs. Meanwhile we also prove when T∗<+∞, the solution must blow up in finite time. On the other hand, we prove that the solution decays at an exponential rate and the two free boundaries converge to a finite limit provided the initial datum is small sufficiently. AMS Subject Classifications: 35K20, 35R35, 92B05 Chinese Library Classifications: O175\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2020-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4208/jpde.v33.n3.5\",\"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://doi.org/10.4208/jpde.v33.n3.5","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

本文研究了一类具有双自由边界的反应扩散方程ut - duxx = au+∫t 0 u p(x，τ)dτ+k(x)。研究了有限时间内的爆破现象和时间全局解的渐近性质。我们的结果表明，如果∫h0−h0 k(x)ψ1dx足够大，则会发生爆炸。同时也证明了当T * <+∞时，解在有限时间内必须爆破。另一方面，我们证明了在初始基准足够小的情况下，解以指数速率衰减，两个自由边界收敛于有限极限。AMS学科分类:35K20, 35R35, 92B05中文图书馆分类:O175

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

Blowup and Asymptotic Behavior of a Free Boundary Problem with a Nonlinear Memory

In this paper, we investigate a reaction-diffusion equation ut−duxx = au+ ∫ t 0 u p(x,τ)dτ+k(x) with double free boundaries. We study blowup phenomena in finite time and asymptotic behavior of time-global solutions. Our results show if ∫ h0 −h0 k(x)ψ1dx is large enough, then the blowup occurs. Meanwhile we also prove when T∗<+∞, the solution must blow up in finite time. On the other hand, we prove that the solution decays at an exponential rate and the two free boundaries converge to a finite limit provided the initial datum is small sufficiently. AMS Subject Classifications: 35K20, 35R35, 92B05 Chinese Library Classifications: O175

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助