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On a reaction diffusion equation with nonlinear time‐nonlocal source term
Author(s) -
Ahmad Bashir,
Alsaedi Ahmed,
Kirane Mokhtar
Publication year - 2016
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.3473
Subject(s) - mathematics , term (time) , nonlinear system , exponential growth , diffusion , mathematical analysis , reaction–diffusion system , exponential function , evolution equation , diffusion equation , space (punctuation) , spacetime , blowing up , space time , physics , computer science , thermodynamics , economy , quantum mechanics , chemical engineering , engineering , economics , service (business) , operating system
In this article, we prove the local existence of a unique solution to a nonlocal in time and space evolution equation with a time nonlocal nonlinearity of exponential growth. Moreover, under some suitable conditions on the initial data, it is shown that local solutions experience blow‐up. The time profile of the blowing‐up solutions is also presented. Copyright © 2015 John Wiley & Sons, Ltd.