Solvability of superlinear fractional parabolic equations

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

Abstract

We study necessary conditions and sufficient conditions for the existence of local-in-time solutions of the Cauchy problem for superlinear fractional parabolic equations. Our conditions are sharp and clarify the relationship between the solvability of the Cauchy problem and the strength of the singularities of the initial measure.

• Journal Article Type: Article
• Acceptance Date: Nov 2, 2022
• Online Publication Date: Dec 10, 2022
• Publication Date: Mar 1, 2023
• Deposit Date: Nov 15, 2022
• Publicly Available Date: Dec 11, 2023
• Journal: Journal of Evolution Equations
• Print ISSN: 1424-3199
• Electronic ISSN: 1424-3202
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 23
• Issue: 1
• Article Number: 4
• Pages: 4
• DOI: https://doi.org/10.1007/s00028-022-00853-z
• Keywords: superlinear fractional parabolic equations; solvability; optimal singularity, Semilinear parabolic equations
• Public URL: https://uwe-repository.worktribe.com/output/10142314
• Publisher URL: https://link.springer.com/article/10.1007/s00028-022-00853-z