Related papers: FKPP fronts in cellular flows: the large-P\'eclet …
G-equations are well-known front propagation models in turbulent combustion and describe the front motion law in the form of local normal velocity equal to a constant (laminar speed) plus the normal projection of fluid velocity. In level…
We perform a computationl study of front speeds of G-equation models in time dependent cellular flows. The G-equations arise in premixed turbulent combustion, and are Hamilton-Jacobi type level set partial differential equations (PDEs). The…
We study traveling fronts in a system of one dimensional reaction-diffusion-advection equations motivated by problems in reactive flows. In the limit as a parameter tends to infinity, we construct the approximate front profile and determine…
A kinetic approach is adopted to describe the exponential growth of a small deviation of the initial phase space point, measured by the largest Lyapunov exponent, for a dilute system of hard disks, both in equilibrium and in a uniform shear…
Predicting turbulent flame speed (the large time front speed) is a fundamental problem in turbulent combustion theory. Several models have been proposed to study the turbulent flame speed, such as the G-equations, the F-equations…
We study analytically and numerically a model describing front propagation of a KPP reaction in a fluid flow. The model consists of coupled one-dimensional reaction-diffusion equations with different drift coefficients. The main rigorous…
This paper deals with the existence of traveling fronts guided by the medium for a KPP reaction-diffusion equation coming from a model in population dynamics in which there is spatial spreading as well as genetic mutation of a quantitative…
This paper is concerned with spreading properties of space-time heterogeneous Fisher--KPP equations in one space dimension. We focus on the case of everywhere favorable environment with three different zones, a left half-line with slow or…
This paper investigates the existence of generalized transition fronts for Fisher-KPP equations in one-dimensional, almost periodic media. Assuming that the linearized elliptic operator near the unstable steady state admits an almost…
In this paper, we study the spatial propagation dynamics of a parabolic-elliptic chemotaxis system with logistic source which reduces to the well-known Fisher-KPP equation without chemotaxis. It is known that for fast decaying initial…
A numerical study of the role of anomalous diffusion in front propagation in reaction-diffusion systems is presented. Three models of anomalous diffusion are considered: fractional diffusion, tempered fractional diffusion, and a model that…
The propagation of fronts in the Fisher-Kolmogorov equation with spatially varying diffusion coefficients is studied. Using coordinate changes, WKB approximations, and multiple scales analysis, we provide an analytic framework that…
We study the asymptotic behavior of solutions to a monostable integro-differential Fisher-KPP equation , that is where the standard Laplacian is replaced by a convolution term, when the dispersal kernel is fat-tailed. We focus on two…
We study the propagation properties of nonnegative and bounded solutions of the class of reaction-diffusion equations with nonlinear fractional diffusion: $u_{t} + (-\Delta)^s (u^m)=f(u)$. For all $0<s<1$ and $m> m_c=(N-2s)_+/N $, we…
We report on recent progress in the study of nonlinear diffusion equations involving nonlocal, long-range diffusion effects. Our main concern is the so-called fractional porous medium equation, $\partial_t u +(-\Delta)^{s}(u^m)=0$, and some…
In this paper, some properties of the minimal speeds of pulsating Fisher-KPP fronts in periodic environments are established. The limit of the speeds at the homogenization limit is proved rigorously. Near this limit, generically, the fronts…
This paper is concerned with the existence of pulsating travelling fronts for a KPP reaction-diffusion equation posed in a multi-dimensional periodic medium. We provide an alternative proof of the classic existence result. Our proof relies…
Using the time-dependent Ginzburg-Landau equations we study the propagation of planar fronts in superconductors, which would appear after a quench to zero applied magnetic field. Our numerical solutions show that the fronts propagate at a…
In Cao, Du, Li and Li [8], a nonlocal diffusion model with free boundaries extending the local diffusion model of Du and Lin [12] was introduced and studied. For Fisher-KPP type nonlinearities, its long-time dynamical behaviour is shown to…
We investigate properties of the particle distribution near the tip of one-dimensional branching random walks at large times $t$, focusing on unusual realizations in which the rightmost lead particle is very far ahead of its expected…