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On local existence and blowup of solutions for a time‐space fractional diffusion equation with exponential nonlinearity
Author(s) -
Bekkai Achouak,
Rebiai Belgacem,
Kirane Mokhtar
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5476
Subject(s) - mathematics , uniqueness , nonlinear system , mathematical analysis , exponential function , exponential growth , banach space , contraction (grammar) , contraction mapping , contraction principle , function (biology) , space (punctuation) , fixed point theorem , linguistics , philosophy , physics , quantum mechanics , medicine , evolutionary biology , biology
In this paper, we are concerned with local existence and blowup of a unique solution to a time‐space fractional evolution equation with a time nonlocal nonlinearity of exponential growth. At first, we prove the existence and uniqueness of the local solution by the Banach contraction mapping principle. Then, the blowup result of the solution in finite time is established by the test function method with a judicious choice of the test function.