Related papers: Sharp Asymptotics for KPP Pulsating Front Speed-up…
The famous Fisher-KPP reaction diffusion model combines linear diffusion with the typical Fisher-KPP reaction term, and appears in a number of relevant applications. It is remarkable as a mathematical model since, in the case of linear…
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…
Flows in which energy is transported predominantly as Poynting flux are thought to occur in pulsars, gamma-ray bursts and relativistic jets from compact objects. The fluctuating component of the magnetic field in such a flow can in…
In absence of advection, reaction-diffusion systems are able to organize into spatiotemporal patterns, in particular spiral and target waves. Whenever advection is present and can be parameterised in terms of effective or turbulent…
We present a (heuristic) theoretical derivation for the scaling of the diffusion coefficient $D_f$ for fluctuating ``pulled'' fronts. In agreement with earlier numerical simulations, we find that as $N\to\infty$, $D_f$ approaches zero as…
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…
In this paper, the sharp interface limit for the compressible non-isentropic Navier-Stokes/Allen-Cahn system is derived by the method of matched asymptotic expansion. We show that the leading order problem satisfies the compressible…
We consider reaction-diffusion equations of KPP type in a presence of a line of fast diffusion with non-local exchange terms between the line and the framework. Our study deals with the infimum of the spreading speed depending on the…
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…
The paper presents new simple sharp bounds for transition density functions for time-homogeneous diffusions processes. The bounds are obtained under mild conditions on the drift and diffusion coefficients, extending and substantially…
In the present paper we study the fast rotation limit for viscous incompressible fluids with variable density, whose motion is influenced by the Coriolis force. We restrict our analysis to two dimensional flows. In the case when the initial…
We consider in this paper a reaction-diffusion system under a KPP hypothesis in a cylindrical domain in the presence of a shear flow. Such systems arise in predator-prey models as well as in combustion models with heat losses. Similarly to…
The long-time behavior of a reaction-diffusion front between one static (e.g. porous solid) reactant A and one initially separated diffusing reactant B is analyzed for the mean-field reaction-rate density R(\rho_A,\rho_B) =…
This paper is devoted to the study of spatial propagation dynamics of species in locally spatially inhomogeneous patchy environments or media. For a lattice differential equation with monostable nonlinearity in a discrete homogeneous media,…
Radiative transfer in a relativistic plane-parallel flow, e.g., an accretion disk wind, is examined in the fully special relativistic treatment. Under the assumption of a constant flow speed, for the relativistically moving atmosphere we…
We investigate fast diffusions on finite directed graphs. We prove results in a way dual to presented in Bobrowski, A. Ann. Henri Poincar\'e (2012) 13(6): 1501-1510 and Bobrowski, A., Morawska, K. DCDS-B (2012), 17(7): 2313-2327, and obtain…
Invasion waves are a fundamental building block of theoretical ecology. In this study we aim to take the first steps to link propagation failure and fast acceleration of traveling waves to critical transitions (or tipping points). The…
The empirical velocity of a reaction-diffusion front, propagating into an unstable state, fluctuates because of the shot noises of the reactions and diffusion. Under certain conditions these fluctuations can be described as a diffusion…
The famous Fisher-KPP reaction-diffusion model combines linear diffusion with the typical KPP reaction term, and appears in a number of relevant applications in biology and chemistry. It is remarkable as a mathematical model since it…
The main contribution of this paper is twofold: (1) Recently, Iyer, Xu, and Zlato\v{s} studied the dissipation enhancement by cellular flows based on standard advection-diffusion equations via a stochastic method. We generalize their…