On a reaction diffusion equation with nonlinear time-nonlocal source term

Bashir Ahmad; Ahmed Alsaedi; Mokhtar Kirane

doi:10.1002/mma.3473

On a reaction diffusion equation with nonlinear time-nonlocal source term

Bashir Ahmad, Ahmed Alsaedi, Mokhtar Kirane

Mathematics

King Abdulaziz University

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

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.

Original language	British English
Pages (from-to)	236-244
Number of pages	9
Journal	Mathematical Methods in the Applied Sciences
Volume	39
Issue number	2
DOIs	https://doi.org/10.1002/mma.3473
State	Published - 1 Jan 2016

Keywords

35K55
blow-up
blow-up profile
nonlocal evolution equation
subclass34B44

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10.1002/mma.3473

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abstract = "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.",

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AB - 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.

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On a reaction diffusion equation with nonlinear time-nonlocal source term

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Keywords

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