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

Fujishima, Yohei; Hisa, Kotaro; Ishige, Kazuhiro; Laister, Robert

Authors

Yohei Fujishima

Kotaro Hisa

Kazuhiro Ishige



Contributors

Yohei Fujishima
Researcher

Kotaro Hisa
Researcher

Kazuhiro Ishige
Researcher

Abstract

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.

Journal Article Type Article
Acceptance Date Feb 19, 2024
Online Publication Date May 3, 2024
Publication Date Jun 30, 2024
Deposit Date Mar 11, 2024
Publicly Available Date May 4, 2026
Journal Journal des Mathematiques Pures et Appliquees
Print ISSN 0021-7824
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 186
Pages 150-175
DOI https://doi.org/10.1016/j.matpur.2024.04.005
Keywords superlinear fractional parabolic equations; solvability; supercritical nonlinear- ity; dilation-critical singularity 1
Public URL https://uwe-repository.worktribe.com/output/11752935

Files

This file is under embargo until May 4, 2026 due to copyright reasons.

Contact Robert.Laister@uwe.ac.uk to request a copy for personal use.




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