Nonexistence of solutions to parabolic problems with a potential on weighted graphs

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations Pub Date : 2025-09-24 DOI:10.1016/j.jde.2025.113782

Dario D. Monticelli, Fabio Punzo, Jacopo Somaglia

引用次数: 0

Abstract

We investigate nonexistence of nontrivial nonnegative solutions to a class of semilinear parabolic equations with a positive potential, posed on weighted graphs. Assuming an upper bound on the Laplacian of the distance and a suitable weighted space-time volume growth condition, we show that no global solutions exist. We also discuss the optimality of the hypotheses, thus recovering a critical exponent phenomenon of Fujita type.

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加权图上带势抛物型问题解的不存在性

研究了一类带正势的半线性抛物型方程的非平凡非负解的不存在性。假设距离的拉普拉斯函数的上界和合适的加权时空体积增长条件，我们证明了不存在全局解。我们还讨论了假设的最优性，从而恢复了Fujita型的临界指数现象。

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

Journal of Differential Equations 数学-数学

CiteScore

4.40

自引率

8.30%

发文量

543

审稿时长

9 months

期刊介绍： The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools. Research Areas Include: • Mathematical control theory • Ordinary differential equations • Partial differential equations • Stochastic differential equations • Topological dynamics • Related topics