Blowup in L1(Ω)-norm and global existence for time-fractional diffusion equations with polynomial semilinear terms

This article is concerned with semilinear time-fractional diffusion equations with polynomial nonlinearity in a bounded domain with the homogeneous Neumann boundary condition and positive initial values. In the case of , we prove the blowup of solutions in the sense that tends to as approaches some...

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Bibliographic Details
Published in:Advances in nonlinear analysis 2023-12, Vol.12 (1), p.199-204
Main Authors: Floridia, Giuseppe, Liu, Yikan, Yamamoto, Masahiro
Format: Article
Language:English
Subjects:
35B44
35K58
35R11
blowup
global existence
polynomial nonlinearity
semilinear time-fractional diffusion equation
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Summary:This article is concerned with semilinear time-fractional diffusion equations with polynomial nonlinearity in a bounded domain with the homogeneous Neumann boundary condition and positive initial values. In the case of , we prove the blowup of solutions in the sense that tends to as approaches some value, by using a comparison principle for the corresponding ordinary differential equations and constructing special lower solutions. Moreover, we provide an upper bound for the blowup time. In the case of , we establish the global existence of solutions in time based on the Schauder fixed-point theorem.
ISSN:2191-950X
DOI:10.1515/anona-2023-0121