{"title":"Blow-up conditions for a semilinear parabolic system on locally finite graphs","authors":"","doi":"10.1007/s10473-024-0213-0","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>In this paper, we investigate a blow-up phenomenon for a semilinear parabolic system on locally finite graphs. Under some appropriate assumptions on the curvature condition <em>CDE’</em>(<em>n</em>,0), the polynomial volume growth of degree m, the initial values, and the exponents in absorption terms, we prove that every non-negative solution of the semilinear parabolic system blows up in a finite time. Our current work extends the results achieved by Lin and Wu (Calc Var Partial Differ Equ, 2017, 56: Art 102) and Wu (Rev R Acad Cien Serie A Mat, 2021, 115: Art 133).</p>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"25 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Scientia","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10473-024-0213-0","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we investigate a blow-up phenomenon for a semilinear parabolic system on locally finite graphs. Under some appropriate assumptions on the curvature condition CDE’(n,0), the polynomial volume growth of degree m, the initial values, and the exponents in absorption terms, we prove that every non-negative solution of the semilinear parabolic system blows up in a finite time. Our current work extends the results achieved by Lin and Wu (Calc Var Partial Differ Equ, 2017, 56: Art 102) and Wu (Rev R Acad Cien Serie A Mat, 2021, 115: Art 133).
摘要 本文研究了局部有限图上半线性抛物系统的炸毁现象。在曲率条件 CDE'(n,0)、度数为 m 的多项式体积增长、初始值和吸收项指数的一些适当假设下，我们证明了半线性抛物线系统的每个非负解都会在有限时间内炸毁。我们目前的工作扩展了 Lin 和 Wu（Calc Var Partial Differ Equ，2017，56：Art 102）以及 Wu（Rev R Acad Cien Serie A Mat，2021，115：Art 133）取得的成果。
期刊介绍：
Acta Mathematica Scientia was founded by Prof. Li Guoping (Lee Kwok Ping) in April 1981.
The aim of Acta Mathematica Scientia is to present to the specialized readers important new achievements in the areas of mathematical sciences. The journal considers for publication of original research papers in all areas related to the frontier branches of mathematics with other science and technology.
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