On a reaction diffusion equation with nonlinear time‐nonlocal source term |
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| Authors: | Bashir Ahmad Ahmed Alsaedi Mokhtar Kirane |
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| Institution: | 1. NAAM Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia;2. Laboratoire de Mathématiques, Images et Applications, P?le Sciences et Technologies, Université de La Rochelle, La Rochelle, France |
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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. Copyright © 2015 John Wiley & Sons, Ltd. |
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| Keywords: | nonlocal evolution equation blow‐up blow‐up profile subclass34B44 35K55 |
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