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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
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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 $(p,r)=(1+2/N,1)$.

Peer review status:UNDER REVIEW

14 Nov 2021Submitted to Mathematical Methods in the Applied Sciences
15 Nov 2021Assigned to Editor
15 Nov 2021Submission Checks Completed
24 Nov 2021Reviewer(s) Assigned