The Second Critical Exponent for a Time Fractional Reaction-Diffusion Equation

Takefumi Igarashi

doi:10.20944/preprints202407.2242.v1

Preprint Article Version 1 This version is not peer-reviewed

Version 1 : Received: 27 July 2024 / Approved: 27 July 2024 / Online: 29 July 2024 (11:13:35 CEST)

In this paper, we consider the Cauchy problem of a time fractional nonlinear diffusion equation. According to the Kaplan’s first eigenvalue method, we first prove the blow-up of the solutions in finite time for some sufficient conditions. We next give sufficient conditions for the existence of global solutions by using the result of Zhang and Sun. In conclusions, we find the second critical exponent for the existence of global and non-global solutions via the decay rates of the initial data at spatial infinity.

time fractional diffusion equation; blow-up; global existence; critical exponent

Computer Science and Mathematics, Mathematics

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The Second Critical Exponent for a Time Fractional Reaction-Diffusion Equation

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