Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4629187 | Applied Mathematics and Computation | 2013 | 6 Pages |
Abstract
This paper deals with asymptotic behavior of solutions to a reaction-diffusion system coupled via localized and local sources: ut=Îu+vp(xâ(t),t),vt=Îv+uq. 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Jinhuan Wang, Lizhong Zhao, Sining Zheng,