Related papers: Fast reaction limit of reaction-diffusion systems
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…
Reaction-diffusion models have been used over decades to study biological systems. In this context, evolution equations for probability distribution functions and the associated stochastic differential equations have nowadays become…
The primary goal of this paper is to characterize solutions to coupled reaction-diffusion systems. Indeed, we use operators theory to show that under suitable assumptions, then the solutions to the reaction-diffusion equations exist. As…
We investigate the thermodynamic limit of Dicke superradiance. We find an expression for the system's density matrix that we can prove is exact in the limit of large atom numbers N. This is in contrast to previously known solutions whose…
A reaction-diffusion equation is studied in a time-dependent interval whose length varies with time. The reaction term is either linear or of KPP type. On a fixed interval, it is well-known that if the length is less than a certain critical…
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…
The use of fully or partially absorbing boundary conditions for diffusion-based problems has become paradigmatic in physical chemistry and biochemistry to describe reactions occurring in solutions or in living media. However, as chemical…
We study the global existence and uniform-in-time bounds of classical solutions in all dimensions to reaction-diffusion systems dissipating mass. By utilizing the duality method and the regularization of the heat operator, we show that if…
The paper deals with reaction-diffusion equations involving a hysteretic discontinuity in the source term, which is defined at each spatial point. In particular, such problems describe chemical reactions and biological processes in which…
Reaction-diffusion systems, which consist of the reacting particles subject to diffusion process, constitute one of the common examples of non-linear statistical systems. In low space dimensions $d \leq 2$ the usual description by means of…
We consider reaction-diffusion equations of KPP type in a presence of a line of fast diffusion with non-local exchange terms between the line and the framework. Our study deals with the infimum of the spreading speed depending on the…
This paper is concerned with the blow-up property of solutions to an initial boundary value problem for a reaction diffusion equation with special diffusion processes. It is shown, under certain conditions on the initial data, that the…
The close-to-equilibrium regularity of solutions to a class of reaction-diffusion systems is investigated. The considered systems typically arise from chemical reaction networks and satisfy a complex balanced condition. Under some…
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 equation on a 3D thin porous media of thickness $\varepsilon$ which is perforated by periodically distributed cylinders of size $\varepsilon$. On the boundary of the cylinders we prescribe a dynamical…
We concider, the blow-up solutions for a coupled reaction diffusion system with gradient terms. The main purpose is to understand whether the gradient terms effect the blow-up properties. We derive the upper and lower blow-up rate estimates…
We study a two-component reaction-diffusion system in which one of the reaction terms becomes singularly large. Assuming that the initial data are nonnegative and mutually segregated, we prove that the solution converges to that of the heat…
Reaction-diffusion systems offer a powerful framework for understanding self-organized patterns in biological systems, yet controlling these patterns remains a significant challenge. As a consequence, we present a rigorous framework of…
To analyze possible generalizations of reaction-diffusion schemes for the case of subdiffusion we discuss a simple monomolecular conversion A --> B. We derive the corresponding kinetic equations for local A and B concentrations. Their form…
Ordinary differential equations obtained as limits of Markov processes appear in many settings. They may arise by scaling large systems, or by averaging rapidly fluctuating systems, or in systems involving multiple time-scales, by a…