Related papers: Exact Solutions of Low-Dimensional Reaction-Diffus…
Many mathematical models for biological phenomena, such as the spread of diseases, are based on reaction-diffusion equations for densities of interacting cell populations. We present a consistent derivation of reaction-diffusion equations…
We study the diffusion-limited process $A+A\to A$ in one dimension, with finite reaction rates. We develop an approximation scheme based on the method of Inter-Particle Distribution Functions (IPDF), which was formerly used for the exact…
Patterns in reaction-diffusion systems near primary bifurcations can be studied locally and classified by means of amplitude equations. This is not possible for excitable reaction-diffusion systems. In this Letter we propose a global…
In this paper we present computational techniques to investigate the solutions of two-component, nonlinear reaction-diffusion (RD) systems on arbitrary surfaces. We build on standard techniques for linear and nonlinear analysis of RD…
We establish the global existence of weak solutions for a two-species cross-diffusion system, set on the 1-dimensional flat torus, in which the evolution of each species is governed by two mechanisms. The first of these is a diffusion which…
We consider a range of model potentials with metastable states undergoing molecular dynamics coupled to a thermal bath in the high friction regime, and consider how the optimal reaction coordinate depends on the diffusion anisotropy. For…
The exact solution for a system with two-particle annihilation and decoagulation has been studied. The spectrum of the Hamiltonian of the system is found. It is shown that the steady state is two-fold degenerate. The average number density…
We consider conservative cross-diffusion systems for two species where individual motion rates depend linearly on the local density of the other species. We develop duality estimates and obtain stability and approximation results. We first…
We study a two-species reaction-diffusion model where A+A->0, A+B->0 and B+B->0, with annihilation rates lambda0, delta0 > lambda0 and lambda0, respectively. The initial particle configuration is taken to be randomly mixed with mean…
We study an anisotropic, possibly non-homogeneous version of the evolution $p$-Laplacian equation when fast diffusion holds in all directions. We develop the basic theory and prove symmetrization results from which we derive $L^1$ to…
The aim of this work is to study the global existence of solutions for some coupled systems of reaction diffusion which describe the spread within a population of infectious disease. We consider a triangular matrix diffusion and we show…
This paper investigates the dynamics of a reaction-diffusion system with two free boundaries, modeling the invasion of two cooperative species, where the free boundaries represent expanding fronts. We first analyze the long-term behavior of…
We present Monte Carlo results for the two-species trapping reaction $A+B \to B$ with diffusing $A$ and $B$ on lattices in one, two and three dimension. We use a novel algorithm which permits to simulate survival probabilities of $A$ partic…
We derive a class of multi-species aggregation-diffusion systems from stochastic interacting particle systems via relative entropy method with quantitative bounds. We show an algebraic $L^1$-convergence result using moderately interacting…
We resolve a long standing question regarding the suitable effective diffusion coefficient of the spherically-symmetric transport equation, which is valid at long times. To that end, we generalize a transport solution in three dimensions…
We study driven 1d lattice gas models with two types of particles and nearest neighbor hopping. We find the most general case when there is a shock solution with a product measure which has a density-profile of a step function for both…
We consider reaction diffusion systems where components diffuse inside the domain and react on the surface through mass transport type boundary conditions. Under reasonable hypotheses, we establish the existence of component wise…
To capture the dynamic behaviors of reaction-subdiffusion in flow fields, in the present paper we analyze a simple monomolecular conversion A $\rightarrow$ B. We derive the corresponding master equations for the distribution of A and B…
In this paper, we study discrete dynamics of phytoplankton-zooplankton system with Holling type II and Holling type III predator functional responses. The stability of positive fixed points are investigated. By finding invariant sets, the…
We report some basic results regarding transport in disordered reaction-diffusion systems with birth (A->2A), death (A->0), and binary competition (2A->A) processes. We consider a model in which the growth process is only allowed to take…