We study an extension of the classical Fisher-KPP equation to stratified groups. show positivity, boundedness, asymptotic time-behavior, and blow-up in finite time solutions. These results are also discussed for (time-fractional) by means Caputo time-fractional derivative.

We consider a reaction–diffusion equation on 3D thin porous media of thickness $$\varepsilon $$ which is perforated by periodically distributed cylinders size . On the boundary cylinders, we prescribe dynamical condition pure-reactive type. As \rightarrow 0$$ , in 2D limit resulting has source term coming from dynamical-type conditions imposed boundaries original domain.

[1] Particle tracking algorithms are very useful methods to model conservative transport in surface and subsurface hydrological systems. Recently, a novel ad hoc particle-based method was proposed to account for multicomponent reactive transport by Benson and Meerschaert (2008). This one-dimensional particle method has been shown to match theoretical predictions, but, to date, there has been no...

This paper focuses on the low-dimensional representation of multivariate functions. We study a recursive POD representation, based upon the use of the power iterate algorithm to recursively expand the modes retained in the previous step. We obtain general error estimates for the truncated expansion, and prove that the recursive POD representation provides a quasi-optimal approximation in L2 nor...

The reaction-diffusion master equation (RDME) is a lattice stochastic reaction-diffusion model that has been used to study spatially distributed cellular processes. The RDME is often interpreted as an approximation to spatially continuous models in which molecules move by Brownian motion and react by one of several mechanisms when sufficiently close. In the limit that the lattice spacing approa...