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
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
Copyright © 2002 Rigoberto Medina and Sui Sun Cheng. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.