具有非线性边界条件的半线性热方程上爆率和下爆率估计

IF 1.1 Q1 MATHEMATICS

JOURNAL OF INTERDISCIPLINARY MATHEMATICS Pub Date : 2023-01-01 DOI:10.47974/jim-1302

Maan A. Rasheed, M. Chlebík

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引用次数: 0

摘要

本文考虑了一类具有Neumann边界条件的半线性热方程的爆破解，其中在微分方程和边界条件中出现的非线性项为指数型。研究了非线性项对最后爆破行为的影响。准确地说，利用积分方程法和极大原理技术建立了上(下)爆破率估计。结果表明，反应和边界项的存在对上(下)爆破速率估计形式有重要影响。

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Upper and lower blow-up rate estimates of a semilinear heat equation with a nonlinear boundary condition

In this paper, we consider the blow-up solutions of a semi-linear heat equation with a Neumann boundary condition, where the nonlinear terms, appear in the differential equation and in the boundary conditions, are of exponential types. We study the effect of the nonlinear terms on the last blow-up behavior. Precisely, the upper (lower) blow-up rate estimates are established by using integral equation method and maximum principle techniques. The results show that the presentence of the reaction and boundary terms has important effects on the upper (lower) blow-up rate estimates forms.

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来源期刊

JOURNAL OF INTERDISCIPLINARY MATHEMATICS MATHEMATICS-

CiteScore

2.70

自引率

23.50%

发文量

141

期刊介绍： The Journal of Interdisciplinary Mathematics (JIM) is a world leading journal publishing high quality, rigorously peer-reviewed original research in mathematical applications to different disciplines, and to the methodological and theoretical role of mathematics in underpinning all scientific disciplines. The scope is intentionally broad, but papers must make a novel contribution to the fields covered in order to be considered for publication. Topics include, but are not limited, to the following: • Interface of Mathematics with other Disciplines • Theoretical Role of Mathematics • Methodological Role of Mathematics • Interface of Statistics with other Disciplines • Cognitive Sciences • Applications of Mathematics • Industrial Mathematics • Dynamical Systems • Mathematical Biology • Fuzzy Mathematics The journal considers original research articles, survey articles, and book reviews for publication. Responses to articles and correspondence will also be considered at the Editor-in-Chief’s discretion. Special issue proposals in cutting-edge and timely areas of research in interdisciplinary mathematical research are encouraged – please contact the Editor-in-Chief in the first instance.