Related papers: Exact travelling solution for a reaction-diffusion…
We study the persistence and propagation (or blocking) phenomena for a species in periodically hostile environments. The problem is described by a reaction-diffusion equation with zero Dirichlet boundary condition. We first derive the…
We study the existence of traveling waves of reaction-diffusion systems with delays in both diffusion and reaction terms of the form $\partial u(x,t)/\partial t = \Delta u(x,t-\tau_1)+f(u(x,t),u(x,t-\tau_2))$, where $\tau_1,\tau_2$ are…
Reaction diffusion systems with Turing instability and mass conservation are studied. In such systems, abrupt decays of stripes follow quasi-stationary states in sequence. At steady state, the distance between stripes is much longer than…
We construct nontrivial entire solutions for a bistable reaction-diffusion equation in a class of domains that are unbounded in one direction. The motivation comes from recent results of Berestycki, Bouhours, and Chapuisat concerning…
Point-like topological defects are singular configurations that occur in a variety of in and out of equilibrium systems with two-dimensional orientational order. As they are associated with a nonzero circuitation condition, the presence of…
Standard diffusion equation is based on Brownian motion of the dispersing species without considering persistence in the movement of the individuals. This description allows for the instantaneous spreading of the transported species over an…
Reaction-diffusion processes can be adopted to model a large number of dynamics on complex networks, such as transport processes or epidemic outbreaks. In most cases, however, they have been studied from a fermionic perspective, in which…
We study the existence of monotone heteroclinic traveling waves for a general Fisher-Burgers equation with nonlinear and possibly density-dependent diffusion. Such a model arises, for instance, in physical phenomena where a saturation…
We establish the global existence of weak solutions for a two-species cross-diffusion system, set on the 1-dimensional flat torus, in which the evolution of each species is governed by two mechanisms. The first of these is a diffusion which…
We give sufficient conditions for the existence of positive travelling wave solutions for multi-dimensional autonomous reaction-diffusion systems with distributed delay. To prove the existence of travelling waves, we give an abstract…
Superluminal propagation is an intrinsic problem in the diffusion equation and has not been effectively addressed for a long time. In this work, a rigorous solution to this issue is obtained under the assumption that particles undergo a…
Much has been studied on the spreading speed and traveling wave solutions for cooperative reaction-diffusion systems. In this paper, we shall establish the spreading speed for a large class of non-cooperative reaction-diffusion systems and…
We have studied the front propagation in a one dimensional case of combustion by solving numerically an advection-reaction-diffusion equation. The physical model is simplified so that no coupling phenomena are considered and the reacting…
We consider a simple model of particle transport on the line defined by a dynamical map F satisfying F(x+1) = 1 + F(x) for all x in R and F(x) = ax + b for |x| < 0.5. Its two parameters a (`slope') and b (`bias') are respectively symmetric…
In this research note we provide a variational basis for the optimal artificial diffusion method, which has been a cornerstone in developing many stabilized methods. The optimal artificial diffusion method produces exact nodal solutions…
We expand on a previous study of fronts in finite particle number reaction-diffusion systems in the presence of a reaction rate gradient in the direction of the front motion. We study the system via reaction-diffusion equations, using the…
Traveling wave solutions of reaction-diffusion equations are well-studied for Lipschitz continuous monostable and bistable reaction functions. These special solutions play a key role in mathematical biology and in particular in the study of…
Traveling fronts and stationary localized patterns in bistable reaction-diffusion systems have been broadly studied for classical continuous media and regular lattices. Analogs of such non-equilibrium patterns are also possible in networks.…
We establish global-in-time existence results for thermodynamically consistent reaction-(cross-)diffusion systems coupled to an equation describing heat transfer. Our main interest is to model species-dependent diffusivities, while at the…
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…