相关论文: Enhancement of combustion by drift in a coupled re…

We consider an irreversible autocatalytic conversion reaction A+B -> 2A under subdiffusion described by continuous time random walks. The reactants' transformations take place independently on their motion and are described by constant…

We prove the existence of reaction-diffusion traveling fronts in mean zero space-time periodic shear flows for nonnegative reactions including the classical KPP (Kolmogorov-Petrovsky-Piskunov) nonlinearity. For the KPP nonlinearity, the…

This paper investigates the asymptotic behavior of the solutions of the Fisher-KPP equation in a heterogeneous medium, $$\partial_t u = \partial_{xx} u + f(x,u),$$ associated with a compactly supported initial datum. A typical nonlinearity…

We consider a coupled reaction-advection-diffusion system based on the Fisher-KPP and Burgers equations. These equations serve as a one-dimensional version of a model for a reacting fluid in which the arising density differences induce a…

This paper is concerned with transition fronts for reaction-diffusion equations of the Fisher-KPP type. Basic examples of transition fronts connecting the unstable steady state to the stable one are the standard traveling fronts, but the…

In this paper we study the diffusion approximation of a swarming model given by a system of interacting Langevin equations with nonlinear friction. The diffusion approximation requires the calculation of the drift and diffusion coefficients…

We study front propagation in the reaction diffusion process $\{A\stackrel{\epsilon}\to2A, A\stackrel {\epsilon_t}\to3A\}$ on a one dimensional (1d) lattice with hard core interaction between the particles. Using the leading particle…

The empirical velocity of a reaction-diffusion front, propagating into an unstable state, fluctuates because of the shot noises of the reactions and diffusion. Under certain conditions these fluctuations can be described as a diffusion…

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…

Reaction-diffusion systems with cross-diffusion terms in addition to, or instead of, the usual self-diffusion demonstrate interesting features which motivate their further study. The present work is aimed at designing a toy…

This paper is devoted to the analysis of the large-time behavior of solutions of one-dimensional Fisher-KPP reaction-diffusion equations. The initial conditions are assumed to be globally front-like and to decay at infinity towards the…

We study the propagation of pulled fronts in the $A <-> \leftrightarrow A+A$ microscopic reaction-diffusion process using Monte Carlo (MC) simulations. In the mean field approximation the process is described by the deterministic…

In this paper we study the following one-dimensional reaction-diffusion problem $$ u_t+(-\Delta)^s u=f(x-c t, u) \;\:\textrm{ in } \mathbb{R}\times (0,+\infty), $$ where $s>\frac{1}{2}$, $c \in \mathbb{R}$ is a prescribed velocity, and $f$…

We prove stochastic homogenization for reaction-advection-diffusion equations with random space-time-dependent KPP reactions with temporal correlations that are decaying in an appropriate sense. We show that the limiting homogenized dynamic…

We study reaction-diffusion systems where diffusion is by jumps whose sizes are distributed exponentially. We first study the Fisher-like problem of propagation of a front into an unstable state, as typified by the A+B $\to$ 2A reaction. We…

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…

The current paper is devoted to the study of spreading speeds and transition fronts of lattice KPP equations in time heterogeneous media. We first prove the existence, uniqueness, and stability of spatially homogeneous entire positive…

We consider the drift and diffusion properties of periodically driven renewal processes. These processes are defined by a periodically time dependent waiting time distribution, which governs the interval between subsequent events. We show…

In this paper, we prove some qualitative properties of pushed fronts for the periodic reaction-diffusion-equation with general monostable nonlinearities. Especially, we prove the exponential behavior of pushed fronts when they are…

In this paper, we first focus on the speed selection problem for the reaction-diffusion equation of the monostable type. By investigating the decay rates of the minimal traveling wave front, we propose a sufficient and necessary condition…