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.
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