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

IF 0.8 4区数学 Q2 MATHEMATICS

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

Ghassan A. Al-Juaifri, Akil J. Harfash

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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.

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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。

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来源期刊

Georgian Mathematical Journal 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Georgian Mathematical Journal was founded by the Georgian National Academy of Sciences and A. Razmadze Mathematical Institute, and is jointly produced with De Gruyter. The concern of this international journal is the publication of research articles of best scientific standard in pure and applied mathematics. Special emphasis is put on the presentation of results obtained by Georgian mathematicians.