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International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 5, Pages 257-264
http://dx.doi.org/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 Hindawi Publishing Corporation. 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.