Invariant sets and the blow up threshold for coupled systems of reaction–diffusion

Abstract

In this paper, we study a class of semilinear systems of reaction–diffusion on a bounded smooth domain with Dirichlet boundary condition. Applying the potential well method, we find invariant sets for the initial-boundary value problem and derive a threshold of blow up and global existence for its solution.

Keywords:

• system of reaction–diffusion
• potential well method
• global existence
• blow up

AMS Subject Classifications:

• MSC 2010
• 35K57
• 35K20

Acknowledgments

The authors would like to thank the referees for their helpful comments.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 11201025], [grant number 11302024]; the Fundamental Research Funds for Central Universities (FRF-TP-12-106A, FRF-BR-13-023) and Beijing Higher Education Young Elite Teacher Project [grant number YETP0387].