Blowup Analysis for a Nonlocal Diffusion Equation with Reaction and Absorption

We investigate a nonlocal reaction diffusion equation with absorption under Neumann boundary. We obtain optimal conditions on the exponents of the reaction and absorption terms for the existence of solutions blowing up in finite time, or for the global existence and boundedness of all solutions. For...

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Main Authors:	Yulan Wang, Zhaoyin Xiang, Jinsong Hu
Format:	Article
Language:	English
Published:	Hindawi Limited 2012-01-01
Series:	Journal of Applied Mathematics
Online Access:	http://dx.doi.org/10.1155/2012/648067

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spelling	doaj-0eed4e8f318c4bc6b337f460e6b6557f2020-11-24T22:38:16ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/648067648067Blowup Analysis for a Nonlocal Diffusion Equation with Reaction and AbsorptionYulan Wang0Zhaoyin Xiang1Jinsong Hu2School of Mathematics and Computer Engineering, Xihua University, Chengdu 610039, ChinaSchool of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 610054, ChinaSchool of Mathematics and Computer Engineering, Xihua University, Chengdu 610039, ChinaWe investigate a nonlocal reaction diffusion equation with absorption under Neumann boundary. We obtain optimal conditions on the exponents of the reaction and absorption terms for the existence of solutions blowing up in finite time, or for the global existence and boundedness of all solutions. For the blowup solutions, we also study the blowup rate estimates and the localization of blowup set. Moreover, we show some numerical experiments which illustrate our results.http://dx.doi.org/10.1155/2012/648067
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Yulan Wang Zhaoyin Xiang Jinsong Hu
spellingShingle	Yulan Wang Zhaoyin Xiang Jinsong Hu Blowup Analysis for a Nonlocal Diffusion Equation with Reaction and Absorption Journal of Applied Mathematics
author_facet	Yulan Wang Zhaoyin Xiang Jinsong Hu
author_sort	Yulan Wang
title	Blowup Analysis for a Nonlocal Diffusion Equation with Reaction and Absorption
title_short	Blowup Analysis for a Nonlocal Diffusion Equation with Reaction and Absorption
title_full	Blowup Analysis for a Nonlocal Diffusion Equation with Reaction and Absorption
title_fullStr	Blowup Analysis for a Nonlocal Diffusion Equation with Reaction and Absorption
title_full_unstemmed	Blowup Analysis for a Nonlocal Diffusion Equation with Reaction and Absorption
title_sort	blowup analysis for a nonlocal diffusion equation with reaction and absorption
publisher	Hindawi Limited
series	Journal of Applied Mathematics
issn	1110-757X 1687-0042
publishDate	2012-01-01
description	We investigate a nonlocal reaction diffusion equation with absorption under Neumann boundary. We obtain optimal conditions on the exponents of the reaction and absorption terms for the existence of solutions blowing up in finite time, or for the global existence and boundedness of all solutions. For the blowup solutions, we also study the blowup rate estimates and the localization of blowup set. Moreover, we show some numerical experiments which illustrate our results.
url	http://dx.doi.org/10.1155/2012/648067
work_keys_str_mv	AT yulanwang blowupanalysisforanonlocaldiffusionequationwithreactionandabsorption AT zhaoyinxiang blowupanalysisforanonlocaldiffusionequationwithreactionandabsorption AT jinsonghu blowupanalysisforanonlocaldiffusionequationwithreactionandabsorption
_version_	1725713934926741504

Blowup Analysis for a Nonlocal Diffusion Equation with Reaction and Absorption

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