Uniform Blow-Up Rates and Asymptotic Estimates of Solutions for Diffusion Systems with Nonlocal Sources

Cui, Zhoujin; Yang, Zuodong

doi:https://doi.org/10.1155/2007/87696

International Journal of Differential Equations

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Research Article | Open Access

Volume 2007 | Article ID 087696 | https://doi.org/10.1155/2007/87696

Uniform Blow-Up Rates and Asymptotic Estimates of Solutions for Diffusion Systems with Nonlocal Sources

Zhoujin Cui¹and Zuodong Yang^1,2

Academic Editor: Nicola Bellomo

Received13 Apr 2006

Revised27 Nov 2006

Accepted19 Dec 2006

Published13 Feb 2007

Abstract

This paper investigates the local existence of the nonnegative solution and the finite time blow-up of solutions and boundary layer profiles of diffusion equations with nonlocal reaction sources; we also study the global existence and that the rate of blow-up is uniform in all compact subsets of the domain, the blow-up rate of |u(t)|∞ is precisely determined.

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Copyright

Copyright © 2007 Zhoujin Cui and Zuodong Yang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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