Related papers: Minimum wave speeds in monostable reaction-diffusi…
There are a number of situations in which rescaled interacting particle systems have been shown to converge to a reaction diffusion equation (RDE) with a bistable reaction term. These RDEs have traveling wave solutions. When the speed of…
Sufficient conditions for the wave instability in general three-component reaction-diffusion systems are derived. These conditions are expressed in terms of the Jacobian matrix of the uniform steady state of the system, and enable us to…
In this paper, we consider the phenomenon of monostable pulsating fronts for multi-dimensional reaction-diffusion-advection systems in periodic media. Recent results have addressed the existence of pulsating fronts and the linear…
We modify the approach of Burton and Toland [Comm. Pure Appl. Math. (2011)] to show the existence of periodic surface water waves with vorticity in order that it becomes suited to a stability analysis. This is achieved by enlarging the…
Experimental mean flows are commonly used to study wall-bounded turbulence. However, these measurements are often unable to resolve the near-wall region and thus introduce ambiguity in the velocity closest to the wall. This poses a source…
We study a Fisher-KPP equation with spatially periodic diffusion and reaction terms. We identify a class of periodic media for which the equation admits an explicit, closed-form solution. Through a nonlinear change of variables, the problem…
The limits imposed on diffusive shock acceleration by upstream ion-neutral Alfven wave damping, and by ionisation and Coulomb losses of low energy particles, are calculated. Analytic solutions are given for the steady upstream wave…
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…
We deal with the obstacle problem for the porous medium equation in the slow diffusion regime $m>1$. Our main interest is to treat fairly irregular obstacles assuming only boundedness and lower semicontinuity. In particular, the considered…
The numerical analysis of elastic wave propagation in unbounded media may be difficult due to spurious waves reflected at the model artificial boundaries. This point is critical for the analysis of wave propagation in heterogeneous or…
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…
Inspired by one--dimensional light--particle systems, the dynamics of a non-Hamiltonian system with long--range forces is investigated. While the molecular dynamics does not reach an equilibrium state, it may be approximated in the…
We extend to multi-dimensions the work of [1], where new fully explicit kinetic methods were built for the approximation of linear and non-linear convection-diffusion problems. The fundamental principles from the earlier work are retained:…
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…
Dispersive averaging effects are used to show that KdV equation with periodic boundary conditions possesses high frequency solutions which behave nearly linearly. Numerical simulations are presented which indicate high accuracy of this…
The focus of our work is dispersive, second-order effective model describing the low-frequency wave motion in heterogeneous (e.g.~functionally-graded) media endowed with periodic microstructure. For this class of quasi-periodic medium…
We study the space complexity of estimating the diameter of a subset of points in an arbitrary metric space in the dynamic (turnstile) streaming model. The input is given as a stream of updates to a frequency vector $x \in \mathbb{Z}_{\geq…
We present a fast and efficient method for studying vacuum stability constraints in multi-scalar theories beyond the Standard Model. This method is designed for a reliable use in large scale parameter scans. The minimization of the scalar…
We investigate the possibility of stochastic acceleration of background low-energy electrons by turbulent plasma waves. We consider the resonant interaction of the charged particles with all branches of the transverse plasma waves…
e study the minimal wave speed and the asymptotics of the traveling wave solutions of a competitive Lotka Volterra system. The existence of the traveling wave solutions is derived by monotone iteration. The asymptotic behaviors of the wave…