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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…
We consider a diffusion process on an evolving surface with a piecewise Lipschitz-continuous boundary from an energetic point of view. We employ an energetic variational approach with both surface divergence and transport theorems to derive…
Reaction-diffusion equations are widely used as the governing evolution equations for modeling many physical, chemical, and biological processes. Here we derive reaction-diffusion equations to model transport with reactions on a…
We prove existence and uniqueness of a reaction-diffusion equation whose diffusivity is a non-linear functional of the boundary temperature. We do this by studying systems of one-dimensional reflecting diffusions whose noise is a function…
The effects of a boundary on reaction systems are examined in the framework of the general single-species reaction/coalescence process. The boundary naturally represents the reactants' container, but is applicable to exciton dynamics in a…
A horizontal $N$-dimensional plane, having a diffusion of its own, exchanges with the lower half space. There, a reaction-diffusion process, modelled by a free boundary problem, takes place. We wish to understand whether, and how, the free…
The reaction of volatile matter plays an important role in the process of bringing matter from the surface of the planet to the atmosphere. Therefore, by simulating the mixing and chemical reaction process of volatile matter in the…
Second initial boundary problem in narrow domains of width $\epsilon\ll 1$ for linear second order differential equations with nonlinear boundary conditions is considered in this paper. Using probabilistic methods we show that the solution…
We obtain uniform in time bounds for the solutions to a class of thermo-diffusive systems with classical and fractional diffusions. In the classical diffusion case, the nonlinearities are assumed to be at most exponentially growing, while…
In this paper, we study unique, globally defined uniformly bounded weak solutions for a class of semilinear reaction-diffusion-advection systems. The coefficients of the differential operators and the initial data are only required to be…
The paper deals with the homogenization of reaction-diffusion equations with large reaction terms in a multi-scale porous medium. We assume that the fractures and pores are equidistributed and that the coefficients of the equations are…
We develop a theory of reversible diffusion-controlled reactions with generalized binding/unbinding kinetics. In this framework, a diffusing particle can bind to the reactive substrate after a random number of arrivals onto it, with a given…
A generalisation of reaction diffusion systems and their travelling solutions to cases when the productive part of the reaction happens only on a surface in space or on a line on plane but the degradation and the diffusion happen in bulk…
Although the spatially continuous version of the reaction-diffusion equation has been well studied, in some instances a spatially-discretized representation provides a more realistic approximation of biological processes. Indeed,…
We investigate the large time behavior of solutions of reaction-diffusion equations with general reaction terms in periodic media. We first derive some conditions which guarantee that solutions with compactly supported initial data invade…
The trend to equilibrium for reaction-diffusion systems modelling chemical reaction networks is investigated, in the case when reaction processes happen on subsets of the domain. We prove the convergence to equilibrium by directly showing…
We prove a priori bounds for solutions of stochastic reaction diffusion equations with super-linear damping in the reaction term. These bounds provide a control on the supremum of solutions on any compact space-time set which only depends…
In this work, we study the global existence of solutions for a class of semilinear nonlocal reaction-diffusion systems with $m$ components on a bounded domain $\Omega$ in $\mathbb{R}^n$ with smooth boundary. The initial data is assumed to…
The global-in-time existence of renormalized solutions to reaction-cross-diffu-sion systems for an arbitrary number of variables in bounded domains with no-flux boundary conditions is proved. The cross-diffusion part describes the…
We study the asymptotic diffusion processes with (generally nonlocal) open boundaries in one dimension which are exactly solvable by means of the recently developed recursion formula. We investigate the stationary states, which cannot be…