Related papers: Hyperbolic traveling waves driven by growth
This paper is concerned with some nonlinear propagation phenomena for reaction-advection-diffusion equations with Kolmogrov-Petrovsky-Piskunov (KPP) type nonlinearities in general periodic domains or in infinite cylinders with oscillating…
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…
We study the traveling wave solutions to a reaction diffusion system modeling the public goods game with altruistic behaviors. The existence of the waves is derived through monotone iteration of a pair of classical upper- and lower…
We show the relevance of the nonlinear Fisher and Kolmogorov-Petrovsky- Piscounov (KPP) equation to the problem of high energy evolution of the QCD amplitudes. We explain how the traveling wave solutions of this equation are related to…
We study the stability and dynamics of traveling-front solutions of a modified Kuramoto--Sivashinsky equation arising in the modeling of nanoscale ripple patterns that form when a nominally flat solid surface is bombarded with a broad ion…
The Fisher-KPP equation with general nonlinear diffusion and arbitrary kinetic orders in the reaction terms is considered. The existence of oscillatory travelling wave solutions is proved for this model. Conditions for the existence of such…
In Part II of this series of papers, we consider an initial-boundary value problem for the Kolmogorov--Petrovskii--Piscounov (KPP) type equation with a discontinuous cut-off in the reaction function at concentration $u=u_c$. For fixed…
In this paper, we first focus on the speed selection problem for the reaction-diffusion equation of the monostable type. By investigating the decay rates of the minimal traveling wave front, we propose a sufficient and necessary condition…
While there is a long history of employing moving boundary problems in physics, in particular via Stefan problems for heat conduction accompanied by a change of phase, more recently such approaches have been adapted to study biological…
We study a Rock-Paper-Scissors model for competing populations that exhibits travelling waves in one spatial dimension and spiral waves in two spatial dimensions. A characteristic feature of the model is the presence of a robust…
We study multiplicity of the supercritical traveling front solutions for scalar reaction-diffusion equations in infinite cylinders which invade a linearly unstable equilibrium. These equations are known to possess traveling wave solutions…
Biological invasion, whereby populations of motile and proliferative individuals lead to moving fronts that invade into vacant regions, are routinely studied using partial differential equation (PDE) models based upon the classical…
Non-cooperative Fisher-KPP systems with space-time periodic coefficients are motivated for instance by models for structured populations evolving in periodic environments. This paper is concerned with entire solutions describing the…
A nonlinear PDE featuring flux limitation effects together with those of the porous media equation (nonlinear Fokker-Planck) is presented in this paper. We analyze the balance of such diverse effects through the study of the existence and…
We consider a scalar parabolic equation in one spatial dimension. The equation is constituted by a convective term, a reaction term with one or two equilibria, and a positive diffusivity which can however vanish. We prove the existence and…
For a fixed bounded domain $D \subset \mathbb{R}^N$ we investigate the asymptotic behaviour for large times of solutions to the $p$-Laplacian diffusion equation posed in a tubular domain \begin{equation*} \partial_t u = \Delta_p u \quad…
In this work we describe a hyperbolic model with cell-cell repulsion with a dynamics in the population of cells. More precisely, we consider a population of cells producing a field (which we call "pressure") which induces a motion of the…
We consider an evolution equation of parabolic type in R having a travelling wave solution. We perform an appropriate change of variables which transforms the equation into a non local evolution one having a travelling wave solution with…
We obtain a criterion for pulsating front speed-up by general periodic incompressible flows in two dimensions and in the presence of KPP nonlinearities. We achieve this by showing that the ratio of the minimal front speed and the effective…
This paper concerns wave propagation in a class of scalar reaction-diffusion-convection equations with $p$-Laplacian-type diffusion and monostable reaction. We introduce a new concept of a non-smooth traveling wave profile, which allows us…