{"title":"圆柱体中反应-平流-扩散方程发散行波的渐近稳定性","authors":"Fu-Jie Jia, Zhi-Cheng Wang, Gai-Hui Guo","doi":"10.1007/s00033-024-02298-5","DOIUrl":null,"url":null,"abstract":"<p>This paper is devoted to the asymptotic stability of diverging traveling waves for reaction–advection–diffusion equation <span>\\(u_{t}-\\Delta u+\\alpha (t,y)u_{x}=f(t,y,u)\\)</span> in cylinders. By the sliding method, we first establish a Liouville-type result. Then, using the Liouville-type result and truncation technique, we prove the asymptotic stability of the diverging traveling wave.</p>","PeriodicalId":501481,"journal":{"name":"Zeitschrift für angewandte Mathematik und Physik","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The asymptotic stability of diverging traveling waves for reaction–advection–diffusion equations in cylinders\",\"authors\":\"Fu-Jie Jia, Zhi-Cheng Wang, Gai-Hui Guo\",\"doi\":\"10.1007/s00033-024-02298-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>This paper is devoted to the asymptotic stability of diverging traveling waves for reaction–advection–diffusion equation <span>\\\\(u_{t}-\\\\Delta u+\\\\alpha (t,y)u_{x}=f(t,y,u)\\\\)</span> in cylinders. By the sliding method, we first establish a Liouville-type result. Then, using the Liouville-type result and truncation technique, we prove the asymptotic stability of the diverging traveling wave.</p>\",\"PeriodicalId\":501481,\"journal\":{\"name\":\"Zeitschrift für angewandte Mathematik und Physik\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Zeitschrift für angewandte Mathematik und Physik\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s00033-024-02298-5\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Zeitschrift für angewandte Mathematik und Physik","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s00033-024-02298-5","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The asymptotic stability of diverging traveling waves for reaction–advection–diffusion equations in cylinders
This paper is devoted to the asymptotic stability of diverging traveling waves for reaction–advection–diffusion equation \(u_{t}-\Delta u+\alpha (t,y)u_{x}=f(t,y,u)\) in cylinders. By the sliding method, we first establish a Liouville-type result. Then, using the Liouville-type result and truncation technique, we prove the asymptotic stability of the diverging traveling wave.
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