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.

<p style='text-indent:20px;'>We prove existence and uniqueness of <i>eternal solutions</i> in self-similar form growing up time with exponential rate for the weighted reaction-diffusion equation</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \partial_tu = \Delta u^m+|x|^{\sigma}u^p, $\end{document} &l...

We consider a system of coupled reaction-diffusion equations that models the interaction between multiple types of chemical species, particularly the interaction between one messenger RNA and different types of non-coding microRNAs in biological cells. We construct various modeling systems with different levels of complexity for the reaction, nonlinear diffusion, and coupled reaction and diffus...

It may often be tempting to take a fractional diffusion equation and simply create a fractional reactiondiffusion equation by including an additional reaction term of the same form as one would include for a standard Fickian system. However, in real systems, fractional diffusion equations typically arise due to complexity and heterogeneity at some unresolved scales. Thus, while transport of a c...

[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...

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...