Related papers: Asymptotics of Reaction-Diffusion Fronts with One …
We consider non-negative solutions of the fast diffusion equation $u_t=\Delta u^m$ with $m \in (0,1)$, in the Euclidean space R^d, d?3, and study the asymptotic behavior of a natural class of solutions, in the limit corresponding to…
We establish rigorous lower bounds on the speed of traveling fronts and on the bulk burning rate in reaction-diffusion equation with passive advection. The non-linearity is assumed to be of either KPP or ignition type. We consider two main…
A reaction-diffusion model which is called the field-road model was introduced by Berestycki, Roquejoffre and Rossi [9] to describe biological invasion with fast diffusion on a line. In this paper, we investigate this model in a…
Diffusion and reaction of initially separated ions A- and B+ in the presence of counter ions A'+ and B'- is studied. The dynamics is described in terms of reaction-diffusion equations obeying local electroneutrality, and the time-evolution…
Many processes in chemistry, physics, and biology depend on thermally activated events in which the system changes its state by surmounting an activation barrier. Examples range from chemical reactions, protein folding, and nucleation…
Understanding anomalous transport and reaction kinetics due to microscopic physical and chemical disorder is a long-standing goal in many fields including geophysics, biology, and engineering. We consider reaction-diffusion characterized by…
The interaction of a Zeldovich reaction-diffusion front with a localized defect is studied numerically and analytically. For the analysis, we start from conservation laws and develop simple collective variable ordinary differential…
A stress-affected chemical reaction front propagation is considered utilizing the concept of a chemical affinity tensor. A reaction between an elastic solid and diffusing constituents, localized at the reaction front, is considered. As a…
We study the evolution of fronts in a bistable reaction-diffusion system when the nonlinear reaction term is spatially non-homogeneous. This equation has been used to model wave propagation in various biological systems. Extending previous…
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…
We analyse the dynamics of a two dimensional system of interacting active dumbbells. We characterise the mean-square displacement, linear response function and deviation from the equilibrium fluctuation-dissipation theorem as a function of…
We investigate spreading properties of solutions of a large class of two-component reaction-diffusion systems, including prey-predator systems as a special case. By spreading properties we mean the long time behaviour of solution fronts…
A one-dimensional reaction-diffusion model consisting of two species of particles and vacancies on a ring is introduced. The number of particles in one species is conserved while in the other species it can fluctuate because of creation and…
This paper is concerned with reaction-diffusion systems of two symmetric species in spatial dimension one, having two stable symmetric equilibria connected by a symmetric standing front. The first order variation of the speed of this front…
Using pointwise semigroup techniques, we establish sharp rates of decay in space and time of a perturbed reaction diffusion front to its time-asymptotic limit. This recovers results of Sattinger, Henry and others of time-exponential…
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…
We study the kinetics of diffusion-limited coalescence, A+A-->A, and annihilation, A+A-->0, in the Bethe lattice of coordination number z. Correlations build up over time so that the probability to find a particle next to another varies…
We consider a coupled system of two singularly perturbed reaction-diffusion equations, with two small parameters $0< \epsilon \le \mu \le 1$, each multiplying the highest derivative in the equations. The presence of these parameters causes…
We study the long-time behavior of the solutions of a two-component reaction-diffusion system on the real line, which describes the basic chemical reaction $A <=> 2 B$. Assuming that the initial densities of the species $A, B$ are bounded…
The persistence properties of a set of random walkers obeying the A+B -> 0 reaction, with equal initial density of particles and homogeneous initial conditions, is studied using two definitions of persistence. The probability, P(t), that an…