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.
Highlights
Discrete reaction-diffusion type partial difference equations have recently been introduced by a number of authors as models for the study of spatiotemporal chaos
We study nonlinear twolevel partial difference equations and, by means of comparison theorems, we derive sufficient conditions for the solutions to be bounded or to converge to zero
The rest of the proof follows by arguments similar to those in the proof of Theorem 4.1, so we omit it
Summary
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. Our results yield estimates and explicit attractive regions for the solutions.
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