A reaction-diffusion system with mixed-type coupling

作者：Wang, Jinhuan; Zhao, Lizhong; Zheng, Sining^*

来源：Applied Mathematics and Computation, 2013, 219(9): 4219-4224.

DOI：10.1016/j.amc.2012.11.006

• Reaction-diffusion system
• Localized source
• Mixed-type coupling
• Blow-up profile
• Critical Fujita exponent

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.

• 出版日期2013-1-1
• 单位大连理工大学; 辽宁大学