Related papers: Hypocoercivity and reaction-diffusion limit for a …
We study a reaction-diffusion-convection problem with nonlinear drift posed in a domain with periodically arranged obstacles. The non-linearity in the drift is linked to the hydrodynamic limit of a totally asymmetric simple exclusion…
We study the question of periodic homogenization of a variably scaled reaction-diffusion problem with non-linear drift posed for a domain crossed by a flat composite thin layer. The structure of the non-linearity in the drift was obtained…
In this article we deduce a mathematical model of Maxwell-Stefan type for a reactive mixture of polyatomic gases with a continuous structure of internal energy. The equations of the model are derived in the diffusive limit of a kinetic…
We revisit a classical continuum model for the diffusion of multiple species with size-exclusion constraint, which leads to a degenerate nonlinear cross-diffusion system. The purpose of this article is twofold: first, it aims at a…
We perform a fast-reaction limit for a linear reaction-diffusion system consisting of two diffusion equations coupled by a linear reaction. We understand the linear reaction-diffusion system as a gradient flow of the free energy in the…
In this paper, we propose a tumor growth model to incorporate and investigate the spatial effects of autophagy. The cells are classified into two phases: normal cells and autophagic cells, whose dynamics are also coupled with the nutrients.…
We investigate a fast-reaction--diffusion system modelling the effect of autotoxicity on plant-growth dynamics, in which the fast-reaction terms are based on the dichotomy between healthy and exposed roots depending on the toxicity. The…
A space discrete approximation to a highly nonlinear reaction-diffusion system endowed with a stochastic dynamical boundary condition is analyzed and the convergence of the discrete scheme to the solution to the corresponding continuum…
We rigorously prove the passage from a Lotka-Volterra reaction-diffusion system towards a cross-diffusion system at the fast reaction limit. The system models a competition of two species, where one species has a more diverse diet than the…
We consider a reaction-diffusion system which may serve as a model for a ferment catalytic reaction in chemistry. The model consists of a system of reaction diffusion equations with unbounded time dependent coefficients and different…
We study a reaction-diffusion system on the real line, where the reactions of the species are given by one reversible reaction according to the mass-action law. We describe different positive limits at both sides of infinity and investigate…
We analyze a reaction-diffusion system describing the growth of microbial species in a model of flocculation type that arises in biology. Existence of global classical positive solutions is proved under general growth assumptions, with…
Cross-diffusion systems are formally derived from multispecies kinetic models in the diffusion limit. The first limit in the multispecies BGK model of Gross and Krook leads to a variant of the non-isothermal Maxwell-Stefan equations. The…
This work presents algebraic closure models associated with advective transport and nonlinear reactions in a Reynolds-averaged Navier-Stokes context for a system of species subject to binary reactions and transport by advection and…
The macroscopic behavior of the solution of a coupled system of partial differential equations arising in the modeling of reaction-diffusion processes in periodic porous media is analyzed. Our mathematical model can be used for studying…
We propose a mathematical model, namely a reaction-diffusion system, to describe social behaviour of cockroaches. An essential new aspect in our model is that the dispersion behaviour due to overcrowding effect is taken into account {as a…
We prove a global existence, uniqueness and regularity result for a two-species reaction-diffusion volume-surface system that includes nonlinear bulk diffusion and nonlinear (weak) cross diffusion on the active surface. A key feature is a…
In this paper, we study a parabolic reaction diffusion system with constraints that model biofilm growth. Within a unified framework encompassing multiple numerical schemes, we derive the first general convergence rates for approximating…
In this paper, we are concerned with a reaction diffusion system arising from a nuclear reactor model in bounded domains with nonlinear boundary conditions. We show the existence of a stationary solution and its ordered uniqueness. It is…
We consider a kinetic model for a two component gas mixture without chemical reactions. Our goal is to study hypocoercivity for the linearized BGK model for gas mixtures in continuous phase space. By constructing an entropy functional, we…