Electron. J. Diff. Equ., Vol. 2016 (2016), No. 156, pp. 1-11.

Invariant regions and existence of global solutions to reaction-diffusion systems without conditions on the growth of nonlinearities

Samir Bendoukha, Salem Abdelmalek

This article concerns the existence of global solutions for a coupled 2-component reaction diffusion system with a full matrix diffusion and exponential nonlinearities. We show that some results of global and bounded solutions are established via invariant regions and the Lyapunov functional. A numerical example is used to illustrate our results.

Submitted May 2, 2016. Published June 21, 2016.
Math Subject Classifications: 35K45, 35K57.
Key Words: Reaction-diffusion system; global solution, Lyapunov functional.

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Samir Bendoukha
Electrical Engineering Department
College of Engineering at Yanbu
Taibah University, Saudi Arabia
email: sbendoukha@taibahu.edu.sa
Salem Abdelmalek
Department of Mathematics
College of Sciences, Yanbu
Taibah University, Saudi Arabia
email: sallllm@gmail.com

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