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Solvability for time-fractional semilinear parabolic equations with singular initial data
  • Marius Ghergu,
  • Yasuhito Miyamoto,
  • Masamitsu Suzuki
Marius Ghergu
University College Dublin

Corresponding Author:marius.ghergu@ucd.ie

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Yasuhito Miyamoto
The University of Tokyo
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Masamitsu Suzuki
The University of Tokyo
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Abstract

We discuss the existence and nonexistence of a local and global-in-time solution to the fractional problem $$ ¥begin{cases} ¥partial_t^{¥alpha}u=¥Delta u+f(u) & x¥in¥Omega,¥ 01$ one has $|f(¥xi)-f(¥eta)|¥le C(1+|¥xi|+|¥eta|)^{p-1}|¥xi-¥eta|$ for all $¥xi, ¥eta¥in ¥R$. Particular attention is paid to the doubly critical case $(p,r)=(1+2/N,1)$.
14 Nov 2021Submitted to Mathematical Methods in the Applied Sciences
15 Nov 2021Submission Checks Completed
15 Nov 2021Assigned to Editor
24 Nov 2021Reviewer(s) Assigned
24 Jun 2022Review(s) Completed, Editorial Evaluation Pending
25 Jun 2022Editorial Decision: Revise Minor
25 Jul 20221st Revision Received
26 Jul 2022Submission Checks Completed
26 Jul 2022Assigned to Editor
27 Jul 2022Reviewer(s) Assigned
18 Aug 2022Review(s) Completed, Editorial Evaluation Pending
18 Nov 2022Editorial Decision: Accept
09 Dec 2022Published in Mathematical Methods in the Applied Sciences. 10.1002/mma.8933