We consider a reaction-diffusion equation of the type ∂tψ=∂x2ψ+V(ψ)+λσ(ψ)W˙on(0,∞)×T, subject to “nice” initial value and periodic boundary, where T=[−1,1] W˙ denotes space-time white noise. The reaction term V:R→R belongs large family functions that includes Fisher–KPP nonlinearities [V(x)=x(1−x)] as well Allen-Cahn potentials [V(x)=x(1−x)(1+x)], multiplicative nonlinearity σ:R→R is non random...

The reaction-diffusion master equation is a stochastic model often utilized in the study of biochemical reaction networks in living cells. It is applied when the spatial distribution of molecules is important to the dynamics of the system. A viable approach to resolve the complex geometry of cells accurately is to discretize space with an unstructured mesh. Diffusion is modeled as discrete jump...