Nonequilibrium potential for a reaction-diffusion model: Critical behavior and decay of extended metastable states

We study a piecewise linear version of a bistable reaction-diffusion model of an electrothermal instability: the Ballast model. Our aim is to analyze the change in the relative stability of nonhomogeneous linearly stable states as some parameters-boundary reflectivity and system size-are varied, as well as the critical-like behavior when some of these states coalesce. The analysis is carried out through the use of the nonequilibrium potential or Lyapunov functional for this system, which also allows us to study the decay of the metastable extended states.