Related papers: Decay Process for Three - Species Reaction - Diffu…
We consider a reaction-diffusion model incorporating the reactions A -> 0, A -> 2A and 2A -> 3A. Depending on the relative rates for sexual and asexual reproduction of the quantity A, the model exhibits either a continuous or first-order…
Many systems that can be described in terms of diffusion-limited `chemical' reactions display non-equilibrium continuous transitions separating active from inactive, absorbing states, where stochastic fluctuations cease entirely. Their…
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…
A reaction-diffusion system with mass conservation modelling cell polarity is considered. A range of the parameters is found where the solution converges exponentially to the constant equilibrium and the $\omega$-limit set of the solution…
The kinetics of single-species annihilation, $A+A\to 0$, is investigated in which each particle has a fixed velocity which may be either $\pm v$ with equal probability, and a finite diffusivity. In one dimension, the interplay between…
We investigate limit models resulting from a dimensional analysis of quite general heterogeneous catalysis models with fast sorption (i.e.\ exchange of mass between the bulk phase and the catalytic surface of a reactor) and fast surface…
We study systems of reaction-diffusion equations with discontinuous spatially distributed hysteresis in the right-hand side. The input of hysteresis is given by a vector-valued function of space and time. Such systems describe hysteretic…
The modelling of linear and nonlinear reaction-subdiffusion processes is more subtle than normal diffusion and causes different phenomena. The resulting equations feature a spatial Laplacian with a temporal memory term through a time…
A mathematical model for emerging contaminants sorption in multispecies biofilms, based on a continuum approach and mass conservation principles is presented. Diffusion of contaminants within the biofilm is described using a…
We study the ABC model (A + B --> 2B, B + C --> 2C, C + A --> 2A), and its counterpart: the three--component neutral drift model (A + B --> 2A or 2B, B + C --> 2B or 2C, C + A --> 2C or 2A.) In the former case, the mean field approximation…
We analyze the mathematical properties of a multi-species biofilm cross-diffusion model together with very general reaction terms and mixed Dirichlet-Neumann boundary conditions on a bounded domain. This model belongs to the class of…
We consider particle systems that are perturbations of the voter model and show that when space and time are rescaled the system converges to a solution of a reaction diffusion equation in dimensions $d \ge 3$. Combining this result with…
We study kinetics of diffusion-limited catalytically-activated $A + B \to B$ reactions taking place in three dimensional systems, in which an annihilation of diffusive $A$ particles by diffusive traps $B$ may happen only if the encounter of…
The extinction transition on a one dimensional heterogeneous substrate with diffusive correlations is studied. Diffusively correlated heterogeneity is shown to affect the location of the transition point, as the reactants adapt to the…
We describe the construction of a conserved reaction-diffusion system that exhibits self-organized critical (avalanche-like) behavior under the action of a slow addition of particles. The model provides an illustration of the general…
We consider a generalized degenerate diffusion equation with a reaction term $u_t=[A(u)]_{xx}+f(u)$, where $A$ is a smooth function satisfying $A(0)=A'(0)=0$ and $A(u),\ A'(u),\ A''(u)>0$ for $u>0$, $f$ is of monostable type in $[0,s_1]$…
We study reaction-diffusion systems where diffusion is by jumps whose sizes are distributed exponentially. We first study the Fisher-like problem of propagation of a front into an unstable state, as typified by the A+B $\to$ 2A reaction. We…
We consider a reaction-diffusion system including discontinuous hysteretic relay operators in reaction terms. This system is motivated by an epigenetic model that describes the evolution of a population of organisms which can switch their…
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…
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…