Global stability of stationary patterns in bistable reaction-diffusion systems
Open Access
- 1 July 1995
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 52 (1) , 129-136
- https://doi.org/10.1103/physreve.52.129
Abstract
We study a piecewise linear version of a one-component, one-dimensional reaction-diffusion bistable model, with the aim of analyzing the effect of boundary conditions on the formation and stability of stationary patterns. The analysis proceeds through the study of the behavior of the Lyapunov functional in terms of a control parameter: the reflectivity at the boundary. We show that, in this example, this functional has a very simple and direct geometrical interpretation.Keywords
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