Related papers: Front selection in reaction-diffusion systems via …
We investigate the large time behavior of solutions of reaction-diffusion equations with general reaction terms in periodic media. We first derive some conditions which guarantee that solutions with compactly supported initial data invade…
We model the growth, dispersal and mutation of two phenotypes of a species using reaction-diffusion equations, focusing on the biologically realistic case of small mutation rates. After verifying that the addition of a small linear mutation…
A study of a stable front propagating in a turbulent medium is presented. The front is generated through a reaction-diffusion equation, and the turbulent medium is statistically modeled using a Langevin equation. Numerical simulations…
We study the propagation speed of bistable traveling waves in the classical two-component diffusive Lotka-Volterra system under strong competition. From an ecological perspective, the sign of the propagation speed determines the long-term…
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…
Mathematical models describing the spatial spreading and invasion of populations of biological cells are often developed in a continuum modelling framework using reaction-diffusion equations. While continuum models based on linear diffusion…
We consider a stochastically perturbed reaction diffusion equation in a bounded interval, with boundary conditions imposing the two stable phases at the endpoints. We investigate the asymptotic behavior of the front separating the two…
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 study the front propagation in Reaction-Diffusion systems whose reaction dynamics exhibits an unstable fixed point and chaotic or noisy behaviour. We have examined the influence of chaos and noise on the front propagation speed and on…
We consider a class of singularly perturbed 2-component reaction-diffusion equations which admit bistable traveling front solutions, manifesting as sharp, slow-fast-slow, interfaces between stable homogeneous rest states. In many example…
We analyze the stability and dynamics of bistable planar fronts in multicomponent reaction-diffusion systems on $\mathbb{R}^{d}$. Under standard spectral stability assumptions, we establish Lyapunov stability of the front against fully…
We consider planar traveling fronts between stable steady states in two-component singularly perturbed reaction-diffusion-advection equations, where a small quantity $\delta^2$ represents the ratio of diffusion coefficients. The fronts…
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…
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…
The system under study is a reaction-diffusion equation in a horizontal strip, coupled to a diffusion equation on its upper boundary via an exchange condition of the Robin type. This class of models was introduced by H. Berestycki, L. Rossi…
Propagating fronts arising from bistable reaction-diffusion equations are a purely deterministic effect. Stochastic reaction-diffusion processes also show front propagation which coincides with the deterministic effect in the limit of small…
In this paper we study the invasion fronts of spatially periodic monotone reaction-diffusion systems in a multi-dimensional setting. We study the pulsating traveling waves that connect the trivial equilibrium, for which all components of…
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…
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…
The position of a reaction front, propagating into a metastable state, fluctuates because of the shot noise of reactions and diffusion. A recent theory [B. Meerson, P.V. Sasorov, and Y. Kaplan, Phys. Rev. E 84, 011147 (2011)] gave a closed…