The Second Critical Exponent for a Time-Fractional Reaction-Diffusion Equation

IF 2.3 3区数学 Q1 MATHEMATICS

Mathematics Pub Date : 2024-09-17 DOI:10.3390/math12182895

Takefumi Igarashi

引用次数: 0

Abstract

In this paper, we consider the Cauchy problem of a time-fractional nonlinear diffusion equation. According to Kaplan’s first eigenvalue method, we first prove the blow-up of the solutions in finite time under some sufficient conditions. We next provide sufficient conditions for the existence of global solutions by using the results of Zhang and Sun. In conclusion, we find the second critical exponent for the existence of global and non-global solutions via the decay rates of the initial data at spatial infinity.

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时间分数反应-扩散方程的第二临界指数

本文考虑了时间分数非线性扩散方程的 Cauchy 问题。根据 Kaplan 的第一特征值方法，我们首先证明了在某些充分条件下有限时间内解的炸毁。接下来，我们利用 Zhang 和 Sun 的结果为全局解的存在提供了充分条件。最后，我们通过空间无穷大处初始数据的衰减率，找到了全局解和非全局解存在的第二个临界指数。

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

Mathematics Mathematics-General Mathematics

CiteScore

4.00

自引率

16.70%

发文量

4032

审稿时长

21.9 days

期刊介绍： Mathematics (ISSN 2227-7390) is an international, open access journal which provides an advanced forum for studies related to mathematical sciences. It devotes exclusively to the publication of high-quality reviews, regular research papers and short communications in all areas of pure and applied mathematics. Mathematics also publishes timely and thorough survey articles on current trends, new theoretical techniques, novel ideas and new mathematical tools in different branches of mathematics.