Related papers: Diffusive relaxation to equilibria for an extended…
Multiple time scales problems are investigated by combining geometrical and analytical approaches. More precisely, for fast-slow reaction-diffusion systems, we first prove the existence of slow manifolds for the abstract problem under the…
We report exact results for one-dimensional reaction-diffusion models A+A -> inert, A+A -> A, and A+B -> inert, where in the latter case like particles coagulate on encounters and move as clusters. Our study emphasized anisotropy of hopping…
We analyze semilinear reaction-diffusion systems that are mass controlled, and have nonlinearities that satisfy critical growth rates. The systems under consideration are only assumed to satisfy natural assumptions, namely the preservation…
A spatio-temporal evolution of chemicals appearing in a reversible enzyme reaction and modelled by a four component reaction-diffusion system with the reaction terms obtained by the law of mass action is considered. The large time behaviour…
The dynamic response of an interacting electron system is determined by an extension of the relaxation-time approximation forced to obey local conservation laws for number, momentum and energy. A consequence of these imposed constraints is…
An expression for the two-particle relaxation time of collective excitations on a distorted Fermi surface in the diffusion approach to kinetic theory is obtained. The general case of momentum-dependent diffusion and drift coefficients is…
A two species reaction-diffusion model, in which particles diffuse on a one-dimensional lattice and annihilate when meeting each other, has been investigated. Mean field equations for general choice of reaction rates have been solved…
The relation between relaxation and diffusion is investigated in a Hamiltonian system of globally coupled rotators. Diffusion is anomalous if and only if the system is going towards equilibrium. The anomaly in diffusion is not anomalous…
Numerical simulations of a simple reaction--diffusion model reveal a surprising variety of irregular spatio--temporal patterns. These patterns arise in response to finite--amplitude perturbations. Some of them resemble the steady irregular…
We consider a class of macroscopic models for the spatio-temporal evolution of urban crime, as originally going back to Short et al. (Math. Mod. Meth. Appl. Sci. 18, 2008). The focus here is on the question how far a certain nonlinear…
We introduce novel approximate systems for dispersive and diffusive-dispersive equations with nonlinear fluxes. For purely dispersive equations, we construct a first-order, strictly hyperbolic approximation. Local well-posedness of smooth…
A multi-phase-field model for the description of the discontinuous precipitation reaction is formulated which takes into account surface diffusion along grain boundaries and interfaces as well as volume diffusion. Simulations reveal that…
In this paper we consider a simple two patch reaction diffusion model with strong Allee effect, sufficiently distinct carrying capacities, similar reaction strengths, and strong diffusion. In the homogeneous case, i.e., in in the case of…
We present in this work a very short proof for the existence, uniqueness and smoothness in dimensions $d\leq 3$ of the system of reaction diffusion $ \partial\_t a\_i - d\_i \Delta a\_i = (-1)^i (a\_1 a\_3 - a\_2 a\_4)$, where $a\_i \geq 0$…
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…
We study the diffusive expansion for solutions around Maxwellian equilibrium and in a periodic box to the Vlasov-Maxwell-Boltzmann system, the most fundamental model for an ensemble of charged particles. Such an expansion yields a set of…
The macroscopic behavior of the solution of a coupled system of partial differential equations arising in the modeling of reaction-diffusion processes in periodic porous media is analyzed. Our mathematical model can be used for studying…
We consider diffusion-limited reactions A_i + A_j -> 0 (1 <= i < j <= q) in d space dimensions. For q > 2 and d >= 2 we argue that the asymptotic density decay for such mutual annihilation processes with equal rates and initial densities is…
We extend the energetic variational approach so it can be applied to a chemical reaction system with general mass action kinetics. Our approach starts with an energy-dissipation law. We show that the chemical equilibrium is determined by…
Although the spatially continuous version of the reaction-diffusion equation has been well studied, in some instances a spatially-discretized representation provides a more realistic approximation of biological processes. Indeed,…