Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction–diffusion processes are widely used to model such behaviour ...

Reaction-diffusion equations underpin the modelling of a vast array of natural and engineered phenomena, ranging from the spread of invasive species and epidemic outbreaks to phase transitions in ...

The forward and backward conditioned diffusion equations relative to the event of the process attaining absorption in one of the boundaries have been derived from the corresponding Kolmogorov ...

We consider one-dimensional reaction-diffusion equations for a large class of spatially periodic nonlinearities – including multi-stable ones – and study the asymptotic behavior of solutions with ...

This paper develops two local mesh-free methods for designing stencil weights and spatial discretization, respectively, for parabolic partial differential equations (PDEs) of ...