Global attractors and exponential stability of partly dissipative reaction diffusion systems with exponential growth nonlinearity

Abstract

We study the long-time behavior of the solutions of the partly dissipative reaction diffusion systems of the FitzHugh–Nagumo type with exponential growth nonlinearity. More precisely, we prove the existence of weak solutions, the regularity of the global attractor and the exponential stability of stationary solutions of the systems.

Keywords:

• Global attractor
• partly dissipative reaction diffusion system
• exponential growth nonlinearity
• exponential stability

2010 Mathematics Subject Classifications:

• 35A01
• 35B41
• 35B35
• 34K21

Acknowledgements

The authors wish to thank the referee for his/her useful comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

First author is supported by the National Research Foundation of Korea (NRF) grant funded by the 2019R1A2C1002150.