Related papers: Asymptotic expansion for reversible A + B <-> C re…
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…
The convergence to equilibrium of mass action reaction-diffusion systems arising from networks of chemical reactions is studied. The considered reaction networks are assumed to satisfy the detailed balance condition and have no boundary…
We study a large class of 1D reaction diffusion models with quenched disorder using a real space renormalization group method (RSRG) which yields exact results at large time. Particles (e.g. of several species) undergo diffusion with random…
Reversible reaction-diffusion systems display anomalous dynamics characterized by a power-law relaxation toward stationarity. In this paper we study in the aging regime the nonequilibrium dynamical properties of some model systems with…
We consider a system of $N$ bosons in the mean-field scaling regime for a class of interactions including the repulsive Coulomb potential. We derive an asymptotic expansion of the low-energy eigenstates and the corresponding energies, which…
We study dynamics of filling of an initially empty finite medium by diffusing particles $A$ and $B$, which arise on the surface upon dissociation of $AB$ molecules, impinging on it with a fixed flux density $I$, and desorb from it by the…
By considering the master equation of the partially asymmetric diffusion process on a one-dimensional lattice, the most general boundary condition (i.e. interactions) for the multi-species reaction-diffusion processes is considered.…
We consider the probability $P(t)$ that a given site remains unvisited by any of a set of random walkers in $d$ dimensions undergoing the reaction $A+A\to0$ when they meet. We find that asymptotically $P(t)\sim t^{-\theta}$ with a universal…
This paper is concerned with the transient dynamics described by the solutions of the reaction-diffusion equations in which the reaction term consists of a combination of a superlinear power-law absorption and a time-independent point…
We present a general method for studying long time asymptotics of nonlinear parabolic partial differential equations. The method does not rely on a priori estimates such as the maximum principle. It applies to systems of coupled equations,…
A complete description of Q-conditional symmetries for two classes of reaction-diffusion-convection equations with power diffusivities is derived. It is shown that all the known results for reaction-diffusion equations with power…
We discuss stationary concentrations of reactants in an A + B -> 0 reaction under subdiffusion and show that they are described by stationary reaction-diffusion equations with a nonlinear diffusion term. We consider stationary profiles of…
We propose a simple model for reaction-diffusion systems with orientational constraints on the reactivity of particles, and map it onto a field theory with upper critical dimension d_c=2. To two-loop level the long-time particle density…
We study the time asymptotic propagation of solutions to the reaction-diffusion cooperative systems with fractional diffusion. We prove that the propagation speed is exponential in time, and we find the precise exponent of propagation. This…
We prove a contraction in $L^1$ property for the solutions of a nonlinear reaction--diffusion system whose special cases include intercellular transport as well as reversible chemical reactions. Assuming the existence of stationary…
We consider a model system consisting of two reaction-diffusion equations, where one species diffuses in a volume while the other species diffuses on the surface which surrounds the volume. The two equations are coupled via a nonlinear…
Most of the previous studies on the well-known Gray-Scott model view it as an irreversible chemical reaction system. In this paper, we derive a four-species reaction-diffusion system using the energetic variational approach based on the law…
In this paper, we first use the super-sub solution method to prove the local exponential asymptotic stability of some entire solutions to reaction diffusion equations, including the bistable and monostable cases. In the bistable case, we…
A number of results for reactions involving subdiffusive species all with the same anomalous exponent gamma have recently appeared in the literature and can often be understood in terms of a subordination principle whereby time t in…
We discuss the structure of radial solutions of some superlinear elliptic equations which model diffusion phenomena when both absorption and production are present. We focus our attention on solutions defined in R (regular) or in R \ {0}…