On local existence and blowup of solutions for a time‐space fractional diffusion equation with exponential nonlinearity

DOI10.1002/MMA.5476zbMath1414.35254OpenAlexW2909285034WikidataQ128505583 ScholiaQ128505583MaRDI QIDQ5380776

Belgacem Rebiai, Achouak Bekkai, Mukhtar Bin Muhammad Kirane

Publication date: 6 June 2019

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mma.5476

zbMATH Keywords

local existence blowup life span nonlocal evolution equation factional derivative

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Nonlinear evolution equations (47J35) Blow-up in context of PDEs (35B44) Fractional partial differential equations (35R11)

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Globally unsolvability of integro-differential diffusion equation and system with exponential nonlinearities ⋮ Time-space fractional diffusion problems: existence, decay estimates and blow-up of solutions ⋮ Existence results for a class of boundary value problems for fractional differential equations ⋮ Sub-diffusion equations with Mittag-Leffler nonlinearity ⋮ Local/global existence analysis of fractional wave equations with exponential nonlinearity ⋮ Global existence, local existence and blow-up of mild solutions for abstract time-space fractional diffusion equations ⋮ A nonlinear fractional diffusion equation: well-posedness, comparison results, and blow-up ⋮ Existence of solutions to a nonlinear fractional diffusion equation with exponential growth

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