Related papers: Variational characterization of the speed of react…
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…
This paper is concerned with the interaction between a planar traveling front and a compact obstacle for monotone bistable reaction-diffusion systems in exterior domains. By constructing appropriate sub- and supersolutions, we first…
In this note, we give constructive upper and lower bounds for the minimal speed of propagation of traveling waves for non-local delayed reaction-diffusion equation.
We introduce a speed selection mechanism for front propagation in reaction-diffusion systems with multiple fields. This mechanism applies to pulled and pushed fronts alike, and operates by restricting the fields to large "finite" intervals…
The aim of this paper is to study the generalized Fisher-KPP equation with nonlocal diffusion. In specific we prove the existence of a critical speed so that traveling front type solutions exist up to this critical speed and non-existence…
We consider travelling wave solutions of the reaction diffusion equation with quintic nonlinearities $u_t = u_{xx} + \mu u (1 -u ) ( 1 +\alpha u + \beta u^2 +\gamma u^3)$. If the parameters $\alpha , \beta$ and $\gamma$ obey a special…
We prove existence, uniqueness, and stability of transition fronts (generalized traveling waves) for reaction-diffusion equations in cylindrical domains with general inhomogeneous ignition reactions. We also show uniform convergence of…
We develop a theory of reversible diffusion-controlled reactions with generalized binding/unbinding kinetics. In this framework, a diffusing particle can bind to the reactive substrate after a random number of arrivals onto it, with a given…
In this paper we investigate the dynamical properties of a spatially periodic reaction-diffusion system {whose reaction terms are of hybrid nature in the sense that they are partly competitive and partly cooperative depending on the value…
We consider one-dimensional reaction-diffusion equations of Fisher-KPP type with random stationary ergodic coefficients. A classical result of Freidlin and Gartner [16] yields that the solutions of the initial value problems associated with…
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 consider a spatially homogeneous advection-diffusion equation in which the diffusion tensor and drift velocity are time-independent, but otherwise general. We derive asymptotic expressions, valid at large distances from a steady point…
We study front propagation in stirred media using a simplified modelization of the turbulent flow. Computer simulations reveal the existence of the two limiting propagation modes observed in recent experiments with liquid phase isothermal…
This paper is concerned with a diffusion-controlled moving-boundary problem in drug dissolution, in which the moving front passes from one medium to another for which the diffusion coefficient is many orders of magnitude smaller. It has…
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 analytically study diffusive particle acceleration in relativistic, collisionless shocks. We find a simple relation between the spectral index s and the anisotropy of the momentum distribution along the shock front. Based on this…
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 establishes the spectral stability in exponentially weighted spaces of smooth traveling monotone fronts for reaction diffusion equations of Fisher-KPP type with nonlinear degenerate diffusion coefficient. It is assumed that the…
We consider positive travelling fronts of the time-delayed reaction-diffusion equation with the monostable birth function. Our main result says that for every fixed and sufficiently large velocity c, the positive travelling front is unique…
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…