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A reaction-diffusion system with mixed-type coupling
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DOI：10.1016/j.amc.2012.11.006.png)
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Abstract
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This paper deals with asymptotic behavior of solutions to a reaction-diffusion system coupled via localized and local sources: u(t) = Delta u + nu(p)(x*(t), t), nu(t) = Delta nu + u(q). Both the initial-boundary problem with null Dirichlet boundary condition and the Cauchy problem are considered to study the interaction between the two kinds of sources. For the initial-boundary problem we prove that the nonglobal solutions blow up everywhere in the bounded domain with uniform blow-up profiles. In addition, it is interesting to observe that the Cauchy problem admits an infinity Fujita exponent, namely, the solutions blow up under any nontrivial and nonnegative initial data whenever pq > 1. All these imply that the blow-up behavior of solutions is governed by the localized source for the two problems with mixed-type coupling. (C) 2012 Elsevier Inc. All rights reserved.
Keywords:
Reaction-diffusion system
Localized source
Mixed-type coupling
Blow-up profile
Critical Fujita exponent
Journal
IF:
3.4
Papers:
2.3W
Citations:
3.3W