Existence and uniqueness of solution for the nonlinear Brusselator system with Robin boundary conditions

Pub Date : 2023-11-19 DOI:10.1515/gmj-2023-2091

Ghassan A. Al-Juaifri, Akil J. Harfash

{"title":"Existence and uniqueness of solution for the nonlinear Brusselator system with Robin boundary conditions","authors":"Ghassan A. Al-Juaifri, Akil J. Harfash","doi":"10.1515/gmj-2023-2091","DOIUrl":null,"url":null,"abstract":"The system of Brusselator-type reaction-diffusion equations (RDs) on open bounded convex domains <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi mathvariant=\"script\">𝒟</m:mi> <m:mo>⊂</m:mo> <m:msup> <m:mi>ℝ</m:mi> <m:mi>d</m:mi> </m:msup> </m:mrow> </m:math> {\\mathcal{D}\\subset\\mathbb{R}^{d}} <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mrow> <m:mi>d</m:mi> <m:mo>≤</m:mo> <m:mn>3</m:mn> </m:mrow> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:math> {(d\\leq 3)} with Robin boundary conditions (Rbcs) has been mathematically analyzed. The Faedo–Galerkin approach is used to demonstrate the global existence and uniqueness of a weak solution to the system. The weak solution’s higher regularity findings are constructed under more regular conditions on the initial data. In addition, continuous dependence on the initial conditions has been proved.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/gmj-2023-2091","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

Abstract

The system of Brusselator-type reaction-diffusion equations (RDs) on open bounded convex domains 𝒟 ⊂ ℝ d

{\mathcal{D}\subset\mathbb{R}^{d}}

( d ≤ 3 )

{(d\leq 3)}

with Robin boundary conditions (Rbcs) has been mathematically analyzed. The Faedo–Galerkin approach is used to demonstrate the global existence and uniqueness of a weak solution to the system. The weak solution’s higher regularity findings are constructed under more regular conditions on the initial data. In addition, continuous dependence on the initial conditions has been proved.

查看原文

微信好友朋友圈 QQ好友复制链接

具有Robin边界条件的非线性Brusselator系统解的存在唯一性

开有界凸域上的brusselator型反应扩散方程(RDs)系统 {\mathcal{D}\subset\mathbb{R}＾{d}} (d≤3) {(d)\leq 3）} 与Robin边界条件(rbc)进行了数学分析。利用Faedo-Galerkin方法证明了系统弱解的全局存在性和唯一性。弱解的高正则性发现是在初始数据更正则的条件下构造的。此外，还证明了对初始条件的连续依赖。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文去求助