Yohei Fujishima
Local solvability and dilation-critical singularities of supercritical fractional heat equations
Fujishima, Yohei; Hisa, Kotaro; Ishige, Kazuhiro; Laister, Robert
Authors
Contributors
Yohei Fujishima
Researcher
Kotaro Hisa
Researcher
Kazuhiro Ishige
Researcher
Dr Robert Laister Robert.Laister@uwe.ac.uk
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.
Citation
Fujishima, Y., Hisa, K., Ishige, K., & Laister, R. (in press). Local solvability and dilation-critical singularities of supercritical fractional heat equations. Journal de Mathématiques Pures et Appliquées,
Journal Article Type | Article |
---|---|
Acceptance Date | Feb 19, 2024 |
Deposit Date | Mar 11, 2024 |
Journal | Journal de Mathématiques Pures et Appliquées |
Print ISSN | 0021-7824 |
Publisher | Elsevier |
Peer Reviewed | Peer Reviewed |
Keywords | superlinear fractional parabolic equations; solvability; supercritical nonlinear- ity; dilation-critical singularity 1 |
Public URL | https://uwe-repository.worktribe.com/output/11752935 |
This file is under embargo due to copyright reasons.
Contact Robert.Laister@uwe.ac.uk to request a copy for personal use.
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