Fujita exponent and blow-up rate for a mixed local and nonlocal heat equation

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications Pub Date : 2025-02-03 DOI:10.1016/j.na.2025.113761

Leandro M. Del Pezzo , Raúl Ferreira

引用次数: 0

Abstract

In this paper we consider the blow-up problem for a mixed local-nonlocal diffusion operator,

u_{t} = a Δ u - b {(- Δ)}^{s} u + u^{p}

We show that the Fujita exponent is given by the nonlocal part,

p_{F} = 1 + 2 s / N

. We also determinate, in some cases, the blow-up rate.

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局部和非局部混合热方程的Fujita指数和爆破率

本文研究了一类混合局部-非局部扩散算子的爆破问题，ut=aΔu−b（−Δ）su+up，证明了Fujita指数由非局部部分pF=1+2s/N给出。在某些情况下，我们还决定了爆炸速率。

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

Nonlinear Analysis-Theory Methods & Applications 数学-数学

CiteScore

3.30

自引率

0.00%

发文量

265

审稿时长

60 days

期刊介绍： Nonlinear Analysis focuses on papers that address significant problems in Nonlinear Analysis that have a sustainable and important impact on the development of new directions in the theory as well as potential applications. Review articles on important topics in Nonlinear Analysis are welcome as well. In particular, only papers within the areas of specialization of the Editorial Board Members will be considered. Authors are encouraged to check the areas of expertise of the Editorial Board in order to decide whether or not their papers are appropriate for this journal. The journal aims to apply very high standards in accepting papers for publication.