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In this paper the travelling wave solutions in the adiabatic model with two-step chain branching reaction mechanism are investigated both numerically and analytically in the limit of equal diffusivity of reactant, radicals and heat. The…

Pattern Formation and Solitons · Physics 2009-11-13 V. V. Gubernov , H. S. Sidhu , G. N. Mercer

In this paper we revisit the existence of traveling waves for delayed reaction diffusion equations by the monotone iteration method. We show that Perron Theorem on existence of bounded solution provides a rigorous and constructive framework…

Dynamical Systems · Mathematics 2008-01-08 Amin Boumenir , Nguyen Van Minh

In this paper, we consider a reaction-diffusion system describing the propagation of flames under the assumption of ignition-temperature kinetics and fractional reaction order. It was shown in [3] that this system admits a traveling front…

Analysis of PDEs · Mathematics 2024-02-29 Amanda Matson , Claude-Michel Brauner , Peter V. Gordon

We consider a reaction-diffusion equation with nonlocal anisotropic diffusion and a linear combination of local and nonlocal monostable-type reactions in a space of bounded functions on $\mathbb{R}^d$. Using the properties of the…

Analysis of PDEs · Mathematics 2018-04-30 Dmitri Finkelshtein , Yuri Kondratiev , Pasha Tkachov

We consider a reaction-diffusion system where some components react and diffuse on the boundary of a region, while other components diffuse in the interior and react with those on the boundary through mass transport. We establish local…

Analysis of PDEs · Mathematics 2015-11-20 Vandana Sharma , Jeff Morgan

We prove that if a solution of an equation of KdV type is bounded above by a traveling wave with an amplitude that decays faster than a given linear exponential then it must be zero. We assume no restrictions neither on the size nor in the…

Analysis of PDEs · Mathematics 2015-06-03 C. E. Kenig , G. Ponce , L. Vega

We study reaction-diffusion equations of various types in the half-space. For bistable reactions with Dirichlet boundary conditions, we prove conditional uniqueness: there is a unique nonzero bounded steady state which exceeds the bistable…

Analysis of PDEs · Mathematics 2020-07-29 Henri Berestycki , Cole Graham

We study the existence of traveling waves of reaction-diffusion systems with delays in both diffusion and reaction terms of the form $\partial u(x,t)/\partial t = \Delta u(x,t-\tau_1)+f(u(x,t),u(x,t-\tau_2))$, where $\tau_1,\tau_2$ are…

Dynamical Systems · Mathematics 2026-04-23 William Barker , Nguyen Van Minh

Continuing our previous study \cite{DJKZ} on the monostable reaction-diffusion-convection equation, we analyze the bistable case under weak regularity assumptions. Our approach applies monostable results on the subintervals where the…

Analysis of PDEs · Mathematics 2026-01-22 Pavel Drábek , Soyeun Jung , Eunkyung Ko , Michaela Zahradníková

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

Travelling waves of densities of binary fluid mixtures are investigated near a critical point. The free energy is considered in a non-local form taking account of the density gradients. The equations of motions are applied to a universal…

Classical Physics · Physics 2011-10-26 Henri Gouin , Augusto Muracchini , Tommaso Ruggeri

Standard diffusion equation is based on Brownian motion of the dispersing species without considering persistence in the movement of the individuals. This description allows for the instantaneous spreading of the transported species over an…

Pattern Formation and Solitons · Physics 2020-07-13 Pushpita Ghosh , Deb Shankar Ray

We consider a bistable ($0\textless{}\theta\textless{}1$ being the three constant steady states) delayed reaction diffusion equation, which serves as a model in population dynamics. The problem does not admit any comparison principle. This…

Analysis of PDEs · Mathematics 2017-12-06 Matthieu Alfaro , Arnaud Ducrot , Thomas Giletti

Reaction-diffusion equations appear in biology and chemistry, and combine linear diffusion with different kind of reaction terms. Some of them are remarkable from the mathematical point of view, since they admit families of travelling waves…

Analysis of PDEs · Mathematics 2019-01-14 Alessandro Audrito

A unified geometric approach for the stability analysis of traveling pulse solutions for reaction-diffusion equations with skew-gradient structure has been established in a previous paper [9], but essentially no results have been found in…

Analysis of PDEs · Mathematics 2020-10-13 Qin Xing

This paper is concerned with the conditions of existence and nonexistence of traveling wave solutions (TWS) for a class of discrete diffusive epidemic models. We find that the existence of TWS is determined by the so-called basic…

Dynamical Systems · Mathematics 2022-03-17 Ran Zhang , Jinliang Wang , Shengqiang Liu

We consider a system of two reaction-diffusion-advection equations describing the one dimensional directed motion of particles with superimposed diffusion and mutual alignment. For this system we show the existence of traveling wave…

Analysis of PDEs · Mathematics 2021-01-19 Heinrich Freistühler , Jan Fuhrmann

Based on a recent work on traveling waves in spatially nonlocal reaction-diffusion equations, we investigate the existence of traveling fronts in reaction-diffusion equations with a memory term. We will explain how such memory terms can…

Analysis of PDEs · Mathematics 2021-04-27 Alexander Mielke , Sina Reichelt

This paper is concerned with traveling waves to an diffusive SIR model with delay placed in the diffusion terms as well as nonlinear incidence rate with delay. Using a cross iteration scheme and partial monotone conditions it will be shown…

Dynamical Systems · Mathematics 2023-10-24 William Kyle Barker

In this paper, we study the stability of traveling wave solutions arising from a credit rating migration problem with a free boundary, After some transformations, we turn the Free Boundary Problem into a fully nonlinear parabolic problem on…

Analysis of PDEs · Mathematics 2024-01-02 Claude-Michel Brauner , Yuchao Dong , Jin Liang , Luca Lorenzi