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We consider the numerical solution of coupled volume-surface reaction-diffusion systems having a detailed balance equilibrium. Based on the conservation of mass, an appropriate quadratic entropy functional is identified and an…
The convergence to equilibrium for renormalised solutions to nonlinear reaction-diffusion systems is studied. The considered reaction-diffusion systems arise from chemical reaction networks with mass action kinetics and satisfy the complex…
We prove existence, uniqueness, and regularity for a reaction-diffusion system of coupled bulk-surface equations on a moving domain modelling receptor-ligand dynamics in cells. The nonlinear coupling between the three unknowns is through…
We consider two volume-surface reaction-diffusion systems arising from cell biology. The first system describes the localisation of the protein Lgl in the asymmetric division of Drosophila SOP stem cells, while the second system models the…
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…
We study the boundedness and convergence to equilibrium of weak solutions to reaction-diffusion systems with nonlinear diffusion. The nonlinear diffusion is of porous medium type and the nonlinear reaction terms are assumed to grow…
In this article we formulate new models for coupled systems of bulk-surface reaction-diffusion equations on stationary volumes. The bulk reaction-diffusion equations are coupled to the surface reaction-diffusion equations through linear…
The convergence to equilibrium of mass action reaction-diffusion systems arising from networks of chemical reactions is studied. The considered reaction networks are assumed to satisfy the detailed balance condition and have no boundary…
The quantitative convergence to equilibrium for reaction-diffusion systems arising from complex balanced chemical reaction networks with mass action kinetics is studied by using the so-called entropy method. In the first part of the paper,…
Large time dynamics of reaction-diffusion systems modeling some irreversible reaction networks are investigated. Depending on initial masses, these networks possibly possess boundary equilibria, where some of the chemical concentrations are…
We study the asymptotic behaviour of a system of nonlinear reaction--diffusion--advection equations in a domain consisting of two bulk regions connected via microscopic channels distributed within a thin membrane. Both the width of the…
As model problem we consider the prototype for flow and transport of a concentration in porous media in an interior domain and couple it with a diffusion process in the corresponding unbounded exterior domain. To solve the problem we…
The rigorous asymptotics from reaction-cross-diffusion systems for three species with known entropy to cross-diffusion systems for two variables is investigated. The equations are studied in a bounded domain with no-flux boundary…
The global existence of renormalised solutions and convergence to equilibrium for reaction-diffusion systems with non-linear diffusion are investigated. The system is assumed to have quasi-positive non-linearities and to satisfy an entropy…
We consider a reaction-diffusion system for two densities lying in adjacent domains of $\mathbb{R}^N$. We treat two configurations: either a cylinder and its complement, or two half-spaces. Diffusion and reaction heterogeneities for the two…
A class of parabolic cross-diffusion systems modeling the interaction of an arbitrary number of population species is analyzed in a bounded domain with no-flux boundary conditions. The equations are formally derived from a random-walk…
We consider a system of reaction-diffusion equations describing the reversible reaction of two species $\mathcal{U}, \mathcal{V}$ forming a third species $\mathcal{W}$ and vice versa according to mass action law kinetics with arbitrary…
We propose a finite volume scheme for a class of nonlinear parabolic equations endowed with non-homogeneous Dirichlet boundary conditions and which admit relative en-tropy functionals. For this kind of models including porous media…
We consider the finite volume approximation of a reaction-diffusion system with fast reversible reaction. We deduce from a priori estimates that the approximate solution converges to the weak solution of the reaction-diffusion problem and…
A one-dimensional cross-diffusion system modeling the transport of vesicles in neurites is analyzed. The equations are coupled via nonlinear Robin boundary conditions to ordinary differential equations for the number of vesicles in the…