Effect of partially reflecting boundary conditions on the decay of metastable rest states in an activator-inhibitor system

We study the effect of the boundary conditions on the spontaneous nucleation and evaporation of excited domains in the bistable regime of an activator-inhibitor stochastic system. In such a regime a quasivariational approximation can be used to obtain the stationary distribution. The nucleation and evaporation rates of the resulting nonuniform structures are investigated using a piecewise-linear dynamics to obtain analytical results.