超临界分式热方程的局部可解性和扩张临界奇点

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS ACS Applied Bio Materials Pub Date : 2024-05-03 DOI:10.1016/j.matpur.2024.04.005

Yohei Fujishima , Kotaro Hisa , Kazuhiro Ishige , Robert Laister

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引用次数: 0

摘要

我们考虑了具有超临界非线性的分数半线性热方程的考希问题，并建立了局部时间内可解性的必要条件和充分条件。我们引入了初始数据的扩张临界奇点（DCS）概念，并证明对于一大类超临界非线性问题，此类奇点总是存在的。此外，我们还提供了此类奇点的精确公式。

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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Local solvability and dilation-critical singularities of supercritical fractional heat equations

We consider the Cauchy problem for fractional semilinear heat equations with supercritical nonlinearities and establish both necessary conditions and sufficient conditions for local-in-time solvability. We introduce the notion of a dilation-critical singularity (DCS) of the initial data and show that such singularities always exist for a large class of supercritical nonlinearities. Moreover, we provide exact formulae for such singularities.

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来源期刊

ACS Applied Bio Materials Chemistry-Chemistry (all)

CiteScore

9.40

自引率

2.10%

发文量

464