{"title":"具有动态边界条件的非局部反应扩散问题的泛吸引子","authors":"S. Boussaïd","doi":"10.37418/amsj.11.9.4","DOIUrl":null,"url":null,"abstract":"A nonlocal reaction-diffusion equation is presented in this article, based on a model proposed by J. Rubinstein and P. Sternberg [6] with a nonlinear strictly monotone operator. A dynamical boundary condition is considered, rather then the usual ones such as Neumann or Dirichlet boundary conditions. The well-posedness and the existence of a universal attractor of this problem, which describes the long time behavior of the solution, are established.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"UNIVERSAL ATTRACTOR FOR A NONLOCAL REACTION-DIFFUSION PROBLEM WITH DYNAMICAL BOUNDARY CONDITIONS\",\"authors\":\"S. Boussaïd\",\"doi\":\"10.37418/amsj.11.9.4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A nonlocal reaction-diffusion equation is presented in this article, based on a model proposed by J. Rubinstein and P. Sternberg [6] with a nonlinear strictly monotone operator. A dynamical boundary condition is considered, rather then the usual ones such as Neumann or Dirichlet boundary conditions. The well-posedness and the existence of a universal attractor of this problem, which describes the long time behavior of the solution, are established.\",\"PeriodicalId\":231117,\"journal\":{\"name\":\"Advances in Mathematics: Scientific Journal\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-09-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Mathematics: Scientific Journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.37418/amsj.11.9.4\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Mathematics: Scientific Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.37418/amsj.11.9.4","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
UNIVERSAL ATTRACTOR FOR A NONLOCAL REACTION-DIFFUSION PROBLEM WITH DYNAMICAL BOUNDARY CONDITIONS
A nonlocal reaction-diffusion equation is presented in this article, based on a model proposed by J. Rubinstein and P. Sternberg [6] with a nonlinear strictly monotone operator. A dynamical boundary condition is considered, rather then the usual ones such as Neumann or Dirichlet boundary conditions. The well-posedness and the existence of a universal attractor of this problem, which describes the long time behavior of the solution, are established.
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