相关论文: Speed Selection Mechanism for Propagating Fronts i…
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 propose certain approach of solving two-dimensional non-stationary and stationary advection-diffusion-reaction boundary value problems through their reduction to the set of corresponding one-dimensional problems. This method leverages…
The morphology of flame fronts propagating in reactive systems comprised of randomly positioned, point-like sources is studied. The solution of the temperature field and the initiation of new sources is implemented using the superposition…
A free boundary diffusive logistic model finds application in many different fields from biological invasion to wildfire propagation. However, many of these processes show a random nature and contain uncertainties in the parameters. In this…
We address the question: Why may reaction-diffusion equations with hysteretic nonlinearities become ill-posed and how to amend this? To do so, we discretize the spatial variable and obtain a lattice dynamical system with a hysteretic…
A new asymptotic method is presented for the analysis of the traveling waves in the one-dimensional reaction-diffusion system with the diffusion with a finite velocity and Kolmogorov-Petrovskii-Piskunov kinetics. The analysis makes use of…
We establish the existence of semi-wavefronts solutions for a non-local delayed reaction-diffusion equation with monostable nonlinearity. The existence result is proved for all speeds $c\geq c_\star$, where the determination of $c_\star$ is…
In the present paper we study stochastic homogenization for reaction-diffusion equations with stationary ergodic reactions. We first show that under suitable hypotheses, initially localized solutions to the PDE asymptotically become…
We investigate a two-component reaction-diffusion system with a slow-fast structure and spatially varying coefficients $f_1$ and $f_2$ appearing in the slow equation. Under mild boundedness and regularity conditions on $f_1$ and $f_2$ the…
A geometrically invariant concept of fast-slow vector fields perturbed by transport terms (describing molecular diffusion processes) is proposed in this paper. It is an extension of our concept of singularly perturbed vector fields to…
Front propagation in a random environment is studied close to the depinning threshold. At zero temperature we show that the depinning force distribution exhibits a universal behavior. This property is used to estimate the velocity of the…
We study reaction-diffusion particle systems with several interaction mechanisms. As the number of particles tends to infinity, the system admits a mean-field limit describing the bulk behaviour. We focus on determining the propagation…
The current paper is devoted to the investigation of wave propagation phenomenon in reaction-diffusion equations with ignition type nonlinearity in time heterogeneous and random media. It is proven that such equations in time heterogeneous…
This article is concerned with a system of semilinear parabolic equations with two free boundaries describing the spreading fronts of the invasive species in a mutualistic ecological model. The local existence and uniqueness of a classical…
We consider spatially discrete bistable reaction-diffusion equations that admit wave front solutions. Depending on the parameters involved, such wave fronts appear to be pinned or to glide at a certain speed. We study the transition of…
This paper is devoted to the study of some qualitative and quantitative aspects of nonlinear propagation phenomena in diffusive media. More precisely, we consider the case a reaction-diffusion equation in a periodic medium with…
A new upscaling procedure that provides 1D representations of 2D mixing-limited reactive transport systems is developed and applied. A key complication with upscaled models in this setting is that the procedure must differentiate between…
The boundary integral method is extended to derive closed integro-differential equations applicable to computation of the shape and propagation speed of a steadily moving spot and to the analysis of dynamic instabilities in the sharp…
We propose a reaction-transport model for CTRW with non-linear reactions and non-exponential waiting time distributions. We derive non-linear evolution equation for mesoscopic density of particles. We apply this equation to the problem of…
We discuss the problem of fronts propagating into metastable and unstable states. We examine the time development of the leading edge, discovering a precursor which in the metastable case propagates out ahead of the front at a velocity more…