Related papers: Accelerated front propagation for monostable equat…
We study existence and stability of travelling waves for nonlinear convection diffusion equations in the 1-D Euclidean space. The diffusion coefficient depends on the gradient in analogy with the p-Laplacian and may be degenerate.…
Reaction-diffusion equations describe various spatially extended processes that unfold as traveling fronts moving at constant velocity. We introduce and solve analytically a model that, besides such fronts, supports solutions advancing as…
This paper is devoted to the investigation of spatial spreading speeds and traveling wave solutions of monostable evolution equations with nonlocal dispersal in time and space periodic habitats. It has been shown in an earlier work by the…
In this paper, we are interested in the properties of solution of the nonlocal equation $$\begin{cases}u_t+(-\Delta)^su=f(u),\quad t>0, \ x\in\mathbb{R}\\ u(0,x)=u_0(x),\quad x\in\mathbb{R}\end{cases}$$ where $0\le u_0<1$ is a Heaviside…
In this paper, we focus on the existence of propagation fronts, solutions to non-local dispersion reaction models. Our aim is to provide a unified proof of this existence in a very broad framework using simple real analysis tools. In…
We are interested in the threshold phenomena for propagation in nonlocal diffusion equations with some compactly supported initial data. In the so-called bistable and ignition cases, we provide the first quantitative estimates for such…
In this paper, we study the spreading properties of the solutions of an integro-differential equation of the form $u_t=J\ast u-u+f(u).$ We focus on equations with slowly decaying dispersal kernels $J(x)$ which correspond to models of…
Fronts that start from a local perturbation and propagate into a linearly unstable state come in two classes: pulled and pushed. ``Pulled'' fronts are ``pulled along'' by the spreading of linear perturbations about the unstable state, so…
This paper is concerned with the propagating speeds of transition fronts in $R^N$ for spatially periodic bistable reaction-diffusion equations. The notion of transition fronts generalizes the standard notions of traveling fronts. Under the…
This paper is concerned with the spatio-temporal dynamics of nonnegative bounded entire solutions of some reaction-diffusion equations in R N in any space dimension N. The solutions are assumed to be localized in the past. Under certain…
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…
We address the problem of a front propagation in chains with a bi-stable nondegenerate on-site potential and a nonlinear gradient coupling. For a generic nonlinear coupling, one encounters a special regime of transitions, characterized by…
This paper is devoted to studying propagation phenomena in integro-differential equations with a weakly degenerate non-linearity. The reaction term can be seen as an intermediate between the classical logistic (or Fisher-KPP) non-linearity…
We study the evolution of fronts in a bistable reaction-diffusion system when the nonlinear reaction term is spatially non-homogeneous. This equation has been used to model wave propagation in various biological systems. Extending previous…
We identify a new mechanism for propagation into unstable states in spatially extended systems, that is based on resonant interaction in the leading edge of invasion fronts. Such resonant invasion speeds can be determined solely based on…
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…
This paper deals with the large time dynamics of bounded solutions of reaction-diffusion equations with unbounded initial support in $\mathbb{R}^N$. We prove a variational formula for the spreading speeds in any direction, and we also…
In this paper, we study the existence and stability of travelling wave solutions of a kinetic reaction-transport equation. The model describes particles moving according to a velocity-jump process, and proliferating thanks to a reaction…
We study nonlinear stability of spatially homogeneous oscillations in reaction-diffusion systems. Assuming absence of unstable linear modes and linear diffusive behavior for the neutral phase, we prove that spatially localized perturbations…
Invasion phenomena for heterogeneous reaction-diffusion equations are contemporary and challenging questions in applied mathematics. In this paper we are interested in the question of spreading for a reaction-diffusion equation when the…