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Local and blowing‐up solutions for a space‐time fractional evolution system with nonlinearities of exponential growth
Author(s) -
Alsaedi Ahmed,
Ahmad Bashir,
Kirane Mokhtar,
Rebiai Belgacem
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.5657
Subject(s) - mathematics , uniqueness , blowing up , initial value problem , banach space , mathematical analysis , exponential growth , exponential function , banach fixed point theorem , life span , space (punctuation) , medicine , gerontology , linguistics , philosophy
Local and blowing‐up solutions for the Cauchy problem for a system of space and time fractional evolution equations with time‐nonlocal nonlinearities of exponential growth are considered. The existence and uniqueness of the local mild solution is assured by the Banach fixed point principle. Then, we establish a blow‐up result by Pokhozhaev capacity method. Finally, under some suitable conditions, an estimate of the life span of blowing‐up solutions is established.