相关论文: Asymptotic study of critical wave fronts for param…

In this paper, we deal with models with Born-Infeld type diffusion and monostable reaction, investigating the effect of the introduction of a convection term on the limit shape of the critical front profile for vanishing diffusion. We first…

A reaction-diffusion model which is called the field-road model was introduced by Berestycki, Roquejoffre and Rossi [9] to describe biological invasion with fast diffusion on a line. In this paper, we investigate this model in a…

For the classical reaction diffusion equation, the priori speed of fronts is determined exactly in the pioneering paper (R.D. Benguria and M.C. Depassier, {\em Commun. Math. Phys.} 175:221--227, 1996) by variational characterization method.…

We study the asymptotic speed of traveling fronts of the scalar reaction diffusion for positive reaction terms and with a diffusion coefficient depending nonlinearly on the concentration and on its gradient. We restrict our study to…

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 consider a class of cooperative reaction-diffusion systems with free boundaries in one space dimension, where the diffusion terms are nonlocal, given by integral operators involving suitable kernel functions, and they are allowed not to…

Reaction-diffusion waves in multiple spatial dimensions advance at a rate that strongly depends on the curvature of the wave fronts. These waves have important applications in many physical, ecological, and biological systems. In this work,…

Analysis of the speed of propagation in parabolic operators is frequently carried out considering the minimal speed at which its traveling waves move. This value depends on the solution concept being considered. We analyze an extensive…

Statistical properties of the front of a semi-infinite system of single-file diffusion (one dimensional system where particles cannot pass each other, but in-between collisions each one independently follow diffusive motion) are…

We study the existence and stability of propagating fronts in Meinhardt's multivariable reaction-diffusion model of branching in one spatial dimension. We identify a saddle-node-infinite-period (SNIPER) bifurcation of fronts that leads to…

We consider a family of controlled reaction-diffusion equations, describing the spatial spreading of an invasive biological species. For a given propagation speed $c\in{I\!\!R}$, we seek a control with minimum cost, which achieves a…

We study the second-order asymptotics around the superdiffusive strong law~\cite{MMW} of a multidimensional driftless diffusion with oblique reflection from the boundary in a generalised parabolic domain. In the unbounded direction we prove…

We consider here a model of accelerating fronts, introduced in [2], consisting of one equation with nonlocal diffusion on a line, coupled via the boundary condition with a reaction-diffusion equation of the Fisher-KPP type in the upper…

We study invasion fronts and spreading speeds in two component reaction-diffusion systems. Using a variation of Lin's method, we construct traveling front solutions and show the existence of a bifurcation to locked fronts where both…

We perform the analysis of a hyperbolic model which is the analog of the Fisher-KPP equation. This model accounts for particles that move at maximal speed $\epsilon^{-1}$ ($\epsilon\textgreater{}0$), and proliferate according to a reaction…

We investigate the propagation of chemical fronts arising in Fisher--Kolmogorov--Petrovskii--Piskunov (FKPP) type models in the presence of a steady cellular flow. In the long-time limit, a steadily propagating pulsating front is…

This paper is devoted to the study of the asymptotic behaviors of the minimal speed of propagation of pulsating traveling fronts solving the Fisher-KPP reaction-advection-diffusion equation within either a large drift, a mixture of large…

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…

On a smooth bounded Euclidean domain, Sobolev-subcritical fast diffusion with vanishing boundary trace is known to lead to finite-time extinction, with a vanishing profile selected by the initial datum. In rescaled variables, we quantify…

We show that propagation speeds in invasion processes modeled by reaction-diffusion systems are determined by marginal spectral stability conditions, as predicted by the marginal stability conjecture. This conjecture was recently settled in…