International Journal of Mathematics and Mathematical Sciences 
Volume 29 (2002), Issue 5, Pages 257-264
doi:10.1155/S0161171202012656

Asymptotic behavior of the solutions of a discrete reaction-diffusion equation

Rigoberto Medina1 and Sui Sun Cheng2

 1Departamento de Ciencias Exactas, Universidad de Los Lagos, Casilla 933, Osorno, Chile
2Department of Mathematics, Tsing Hua University, Hsinchu, Taiwan 30043, China
Received 3 April 2001; Revised 12 July 2001

Abstract

By means of Bihari type inequalities, we derive sufficient conditions for solutions of a discrete reaction-diffusion equation to be bounded or to converge to zero. Asymptotic representation of solutions are also derived. Our results yield estimates and explicit attractive regions for the solutions.