Asymptotic behavior of solutions to a class of coupled nonlinear parabolic systems

Abstract

This paper studies the Cauchy problem to a class of coupled nonlinear parabolic systems and investigates the asymptotic behavior of solutions to the problem. The blow-up theorem of Fujita type is established by the integral estimation and suitable supersolutions. Moreover, the critical Fujita exponent determined by the diffusion and the spatial dimension is given.

Life span of solutions with large initial data for a semilinear parabolic system coupling exponential reaction terms

“…On the other hand, much effort has been devoted to the study of coupled parabolic systems, local and global existence, finite time blowup and blowup rate estimates, etc. We recommend reading the latest results [14,15]. In [16], Zheng and Zhao considered the radially symmetric solutions for the parabolic system…”