Related papers: Field Theory of Propagating Reaction-Diffusion Fro…
This work focuses on dynamics arising from reaction-diffusion equations , where the profile of propagation is no longer characterized by a single front, but by a layer of several fronts which we call a propagating terrace. This means,…
A particle with internal unobserved states diffusing in a force field will generally display effective advection-diffusion. The drift velocity is proportional to the mobility averaged over the internal states, or effective mobility, while…
The question addressed here is the long time evolution of the solutions to a class of one-dimensional reaction-diffusion equations, in which the diffusion is given by an integral operator. The underlying motivation, discussed in the first…
Diffusion processes have been widely used for approximations in the queueing theory. There are different types of diffusion approximations. Among them, we are interested in those obtained through limits of a sequence of models which…
Reaction-diffusion equations are one of the most common mathematical models in the natural sciences and are used to model systems that combine reactions with diffusive motion. However, rather than normal diffusion, anomalous subdiffusion is…
We formulate and compute a class of mean-field information dynamics for reaction-diffusion equations. Given a class of nonlinear reaction-diffusion equations and entropy type Lyapunov functionals, we study their gradient flows formulations…
We study the formation and the evolution of velocity distribution tails for systems with long-range interactions. In the thermal bath approximation, the evolution of the distribution function of a test particle is governed by a…
We consider asymptotic problems concerning the motion of interface separating the regions of large and small values of the solution of a reaction-diffusion equation in the media consisting of domains with different characteristics…
The use of reaction-diffusion models rests on the key assumption that the underlying diffusive process is Gaussian. However, a growing number of studies have pointed out the prevalence of anomalous diffusion, and there is a need to…
This paper is concerned with reaction-diffusion-advection equations in spatially periodic media. Under an assumption of weak stability of the constant states 0 and 1, and of existence of pulsating traveling fronts connecting them, we show…
This paper establishes existence, uniqueness, and an L^1-comparison principle for weak solutions of a PDE system modeling phase transition reaction-diffusion in congested crowd motion. We consider a general reaction term and mixed…
We develop an analytical diffusion-equation-type approximation scheme for the one-dimensional coagulation reaction A+A->A with partial reaction probability on particle encounters which are otherwise hard-core. The new approximation…
Spontaneous pattern formation in living systems is driven by reaction-diffusion chemistry and active mechanics. The feedback between chemical and mechanical forces is often essential to robust pattern formation, yet it remains poorly…
Reaction-diffusion processes are the foundational model for a diverse range of complex systems, ranging from biochemical reactions to social agent-based phenomena. The underlying dynamics of these systems occur at the individual…
Given a large ensemble of interacting particles, driven by nonlocal interactions and localized repulsion, the mean-field limit leads to a class of nonlocal, nonlinear partial differential equations known as aggregation-diffusion equations.…
This paper studies the phenomenon of invasion for heterogeneous reaction-diffusion equations in periodic domains with monostable and combustion reaction terms. We give an answer to a question rised by Berestycki, Hamel and Nadirashvili in…
We consider a system of reaction-diffusion equations with passive advection term and Lewis number not equal to one. Such systems are used to describe chemical reactions in a flow in a situation where temperature and material diffusivities…
We introduce a phase-field model to describe the dynamics of a self-sustaining propagating combustion front within a medium of randomly distributed reactants. Numerical simulations of this model show that a flame front exists for reactant…
We consider one-dimensional reaction-diffusion equations for a large class of spatially periodic nonlinearities (including multistable ones) and study the asymptotic behavior of solutions with Heaviside type initial data. Our analysis…
In this paper, we are interested in a general equation that has finite speed of propagation compatible with Einstein's theory of special relativity. This equation without external force fields has been derived recently by means of optimal…