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In this paper we consider a classical model of gasless combustion in a one dimensional formulation under the assumption of ignition temperature kinetics. We study the propagation of flame fronts in this model when the initial distribution…

Pattern Formation and Solitons · Physics 2024-03-06 Amanda Matson , Leonid Kagan , Claude-Michel Brauner , Gregory Sivashinsky , Peter V. Gordon

The solution h to the Fisher-KPP equation with a steep enough initial condition develops into a front moving at velocity 2, with logarithmic corrections to its position. In this paper we investigate the value h(c t, t) of the solution ahead…

Analysis of PDEs · Mathematics 2023-02-21 Éric Brunet

In this work, we propose an asymptotic preserving scheme for a non-linear kinetic reaction-transport equation, in the regime of sharp interface. With a non-linear reaction term of KPP-type, a phenomenon of front propagation has been proved…

Numerical Analysis · Mathematics 2018-05-23 Hélène Hivert

We establish a new property of Fisher-KPP type propagation in a plane, in the presence of a line with fast diffusion. We prove that the line enhances the asymptotic speed of propagation in a cone of directions. Past the critical angle given…

Analysis of PDEs · Mathematics 2015-01-09 Henri Berestycki , Jean-Michel Roquejoffre , Luca Rossi

This paper investigates the existence of almost periodic traveling fronts for Fisher-KPP lattice equations in one-dimensional almost periodic media. By the Lyapunov exponent of the linearized operator near the unstable steady state, we give…

Analysis of PDEs · Mathematics 2021-04-29 Xing Liang , Hongze Wang , Qi Zhou , Tao Zhou

This paper is concerned with some nonlinear propagation phenomena for reaction-advection-diffusion equations in a periodic framework. It deals with travelling wave solutions of the equation $$u_t =\nabla\cdot(A(z)\nabla u) +q(z)\cdot\nabla…

Analysis of PDEs · Mathematics 2011-04-15 Mohammad El Smaily

We consider the non-local Fisher-KPP equation modeling a population with individuals competing with each other for resources with a strength related to their distance, and obtain the asymptotics for the position of the invasion front…

Analysis of PDEs · Mathematics 2019-11-28 Emeric Bouin , Christopher Henderson , Lenya Ryzhik

We study the long-time behavior of a triangular system of Fisher--KPP type with $k$ interacting components, associated with a reducible multitype branching Brownian motion with $k$ types of particles. For this cascading system, we prove…

Analysis of PDEs · Mathematics 2026-05-28 Alexandra Stavrianidi

The Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) equation provides a mean-field theory of out-of-time-ordered commutators in locally interacting quantum chaotic systems at high energy density; in the systems with power-law interactions, the…

Statistical Mechanics · Physics 2023-01-18 Tianci Zhou , Andrew Y. Guo , Shenglong Xu , Xiao Chen , Brian Swingle

We prove the existence of a family of travelling wave solutions in a variant of the $\textit{Zeldovich-Frank-Kamenetskii (ZFK) equation}$, a reaction-diffusion equation which models the propagation of planar laminar premixed flames in…

Dynamical Systems · Mathematics 2024-11-21 Samuel Jelbart , Kristian Uldall Kristiansen , Peter Szmolyan

We study the front of the solution to the F-KPP equation with randomized non-linearity. Under suitable assumptions on the randomness involving spatial mixing behavior and boundedness, we show that the front of the solution lags at most…

Probability · Mathematics 2022-11-30 Alexander Drewitz , Lars Schmitz

We investigate spreading properties of solutions of a large class of two-component reaction-diffusion systems, including prey-predator systems as a special case. By spreading properties we mean the long time behaviour of solution fronts…

Analysis of PDEs · Mathematics 2019-07-08 Arnaud Ducrot , Thomas Giletti , Hiroshi Matano

Recently we considered a stochastic discrete model which describes fronts of cells invading a wound \cite{KSS}. In the model cells can move, proliferate, and experience cell-cell adhesion. In this work we focus on a continuum description of…

Statistical Mechanics · Physics 2009-11-13 Evgeniy Khain , Leonard M. Sander

Analysis of the speed of propagation in parabolic operators is frequently carried out considering the minimal speed at which its traveling waves move. This value depends on the solution concept being considered. We analyze an extensive…

Analysis of PDEs · Mathematics 2022-07-14 Margarita Arias , Juan Campos

We propose a novel method for establishing the convergence rates of solutions to reaction-diffusion equations to traveling waves. The analysis is based on the study of the traveling wave shape defect function introduced in [2]. It turns out…

Analysis of PDEs · Mathematics 2023-07-20 Jing An , Christopher Henderson , Lenya Ryzhik

We provide an asymptotic analysis of a non-local Fisher-KPP type equation in periodic media and with a non-local stable operator of order $\alpha$ $\in$ (0, 2). We perform a long time-long range scaling in order to prove that the stable…

Analysis of PDEs · Mathematics 2018-12-14 Alexis Léculier

We investigated the propagation of turbulent fronts in pipe flow at high Reynolds numbers by direct numerical simulation. We used a technique combining a moving frame of reference and an artificial damping to isolate the fronts in short…

Fluid Dynamics · Physics 2022-02-09 Kaiwen Chen , Duo Xu , Baofang Song

We construct the traveling wave solutions of an FKPP growth process of two densities of particles, and prove that the critical traveling waves are locally stable in a space where the perturbations can grow exponentially at the back of the…

Analysis of PDEs · Mathematics 2023-08-16 Florian Kreten

By means of a matched asymptotic expansions approach the electrophoretic velocity and zeta potential of a catalytic particle that uniformly releases ions have been investigated. Attention is focused on large, compared to diffuse layer,…

Soft Condensed Matter · Physics 2024-10-15 Evgeny S. Asmolov , Victoria A. Vasileva , Olga I. Vinogradova

We consider a special type of fast reaction-diffusion systems in which the coefficients of the reaction terms of the two substances are much larger than those of the diffusion terms while the diffusive motion to the substrate is negligible.…

Numerical Analysis · Mathematics 2024-04-30 Yu Zhao , Zhennan Zhou