On the semilinear reaction diffusion system arising from nuclear reactors

Abstract

In this work, the initial-boundary value problem for a class of semilinear reaction-diffusion systems is considered. By an abstract fixed point theorem on positive cone together with an accurate a priori estimate, we establish the coexistence of the positive stationary solutions and the uniqueness of ordered positive stationary solutions. Next, we study the global existence and blowup of positive solutions and obtain a threshold result. Finally, we give the blowup rate estimate of positive blowup solutions.

Keywords:

• positive stationary solution
• mapping in cone
• threshold result
• blowup rate

AMS Subject Classifications:

• Primary: 35K57
• Secondary: 35Q99

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China (No.11071119) and Brazilian Research Council (CNPq).