Blow-Up vs. Global Existence for a Fujita-Type Heat Exchanger System

IF 1.9 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Mathematical Analysis Pub Date : 2024-03-13 DOI:10.1137/23m1587440

Samuel Tréton

引用次数: 0

Abstract

SIAM Journal on Mathematical Analysis, Volume 56, Issue 2, Page 2191-2212, April 2024.
Abstract. We analyze a reaction-diffusion system on [math] which models the dispersal of individuals between two exchanging environments for its diffusive component and incorporates a Fujita-type growth for its reactive component. The originality of this model lies in the coupling of the equations through diffusion, which, to the best of our knowledge, has not been studied in Fujita-type problems. We first consider the underlying diffusive problem, demonstrating that the solutions converge exponentially fast towards those of two uncoupled equations, featuring a dispersive operator that is somehow a combination of Laplacians. By subsequently adding Fujita-type reaction terms to recover the entire system, we identify the critical exponent that separates systematic blow-up from possible global existence.

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藤田型热交换器系统的炸裂与全局存在

SIAM 数学分析期刊》，第 56 卷第 2 期，第 2191-2212 页，2024 年 4 月。摘要。我们分析了[math]上的一个反应-扩散系统，该系统的扩散部分模拟了个体在两个交换环境之间的分散，而反应部分则包含了富士达型增长。这个模型的独创性在于通过扩散耦合方程，而据我们所知，在富士达型问题中还没有研究过这种耦合。我们首先考虑了基本的扩散问题，证明解以指数速度向两个非耦合方程的解收敛，其特点是分散算子在某种程度上是拉普拉斯的组合。随后，通过添加富士达型反应项来恢复整个系统，我们确定了临界指数，它将系统性爆炸与可能的全局存在区分开来。

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

SIAM Journal on Mathematical Analysis 数学-应用数学

CiteScore

3.30

自引率

5.00%

发文量

175

审稿时长

12 months

期刊介绍： SIAM Journal on Mathematical Analysis (SIMA) features research articles of the highest quality employing innovative analytical techniques to treat problems in the natural sciences. Every paper has content that is primarily analytical and that employs mathematical methods in such areas as partial differential equations, the calculus of variations, functional analysis, approximation theory, harmonic or wavelet analysis, or dynamical systems. Additionally, every paper relates to a model for natural phenomena in such areas as fluid mechanics, materials science, quantum mechanics, biology, mathematical physics, or to the computational analysis of such phenomena. Submission of a manuscript to a SIAM journal is representation by the author that the manuscript has not been published or submitted simultaneously for publication elsewhere. Typical papers for SIMA do not exceed 35 journal pages. Substantial deviations from this page limit require that the referees, editor, and editor-in-chief be convinced that the increased length is both required by the subject matter and justified by the quality of the paper.