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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…

Analysis of PDEs · Mathematics 2026-01-21 Pavel Drábek , Soyeun Jung , Eunkyung Ko , Michaela Zahradníková

We prove the existence of a traveling wave solution for a boundary reaction diffusion equation when the reaction term is the combustion nonlinearity with ignition temperature. A key role in the proof is plaid by an explicit formula for…

Analysis of PDEs · Mathematics 2011-01-25 L. Caffarelli , A. Mellet , Y. Sire

This paper concerns the existence and properties of traveling wave solutions to reaction-diffusion-convection equations on the real line. We consider a general diffusion term involving the $p$-Laplacian and combustion-type reaction term. We…

Analysis of PDEs · Mathematics 2024-06-26 Pavel Drábek , Michaela Zahradníková

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…

Analysis of PDEs · Mathematics 2020-08-11 Diego Berti , Andrea Corli , Luisa Malaguti

In this note, we give constructive upper and lower bounds for the minimal speed of propagation of traveling waves for non-local delayed reaction-diffusion equation.

Analysis of PDEs · Mathematics 2008-07-16 Maitere Aguerrea , Gabriel Valenzuela

This paper is concerned with the traveling wave solutions of a reaction-diffusion equation with state-dependent delay. When the birth function is monotone, the existence and nonexistence of monotone traveling wave solutions are established.…

Dynamical Systems · Mathematics 2014-10-14 Guo Lin , Haiyan Wang

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

This paper is concerned with the traveling waves of delayed reaction-diffusion systems where the reaction function possesses the mixed quasimonotonicity property. By the so-called monotone iteration scheme and Schauder's fixed point…

Analysis of PDEs · Mathematics 2010-07-21 Canrong Tian , Zhigui Lin

This paper presents results on the unboundedness and minimal speed of traveling wave solutions for a one-dimensional spatial reaction-diffusion equation with an asymptotically linear reaction term and a saturation parameter. By applying a…

Dynamical Systems · Mathematics 2026-05-11 Yu Ichida

We consider quasi-stationary (travelling wave type) solutions to a general nonlinear reaction-convection-diffusion equation with arbitrary, autonomous coefficients. The second order nonlinear equation describing one dimensional travelling…

Mathematical Physics · Physics 2015-11-30 T. Harko , M. K. Mak

We use a geometric approach to prove the existence of smooth travelling wave solutions of a nonlinear diffusion-reaction equation with logistic kinetics and a convex nonlinear diffusivity function which changes sign twice in our domain of…

Analysis of PDEs · Mathematics 2020-09-17 Yifei Li , Peter van Heijster , Robert Marangell , Matthew J. Simpson

We study travelling-wave solutions for a reaction-diffusion system arising as a model for host-tissue degradation by bacteria. This system consists of a parabolic equation coupled with an ordinary differential equation. For large values of…

Analysis of PDEs · Mathematics 2007-05-23 Danielle Hilhorst , John R. King , Matthias Röger

A set of traveling wave solution to convection-reaction-diffusion equation is studied by means of methods of local nonlinear analysis and numerical simulation. It is shown the existence of compactly supported solutions as well as solitary…

Pattern Formation and Solitons · Physics 2015-05-13 Vsevolod A. Vladimirov

The notion of traveling wave, which typically refers to some particular spatio-temporal con- nections between two stationary states (typically, entire solutions keeping the same profile's shape through time), is essential in the…

Analysis of PDEs · Mathematics 2013-04-04 Thomas Giletti

In this paper, we study the existence and stability of travelling wave solutions of a kinetic reaction-transport equation. The model describes particles moving according to a velocity-jump process, and proliferating thanks to a reaction…

Analysis of PDEs · Mathematics 2014-08-12 Emeric Bouin , Vincent Calvez , Grégoire Nadin

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

We investigate the connection between the existence of an explicit travelling wave solution and the travelling wave with minimal speed in a scalar monostable reaction-diffusion equation.

Analysis of PDEs · Mathematics 2020-08-18 Elaine C. M. Crooks , Michael Grinfeld

We prove existence and uniqueness of travelling waves for a reaction-diffusion system coupling a classical reaction-diffusion equation in a strip with a diffusion equation on a line. To do this we use a continuation method which leads to…

Analysis of PDEs · Mathematics 2014-10-20 Laurent Dietrich

We investigate traveling wave solutions for a nonlinear system of two coupled reaction-diffusion equations characterized by double degenerate diffusivity: \[n_t= -f(n,b), \quad b_t=[g(n)h(b)b_x]_x+f(n,b).\] These systems mainly appear in…

Analysis of PDEs · Mathematics 2024-04-30 Eduardo Muñoz-Hernández , Elisa Sovrano , Valentina Taddei

We study the existence of particular traveling wave solutions of a nonlinear parabolic degenerate diffusion equation with a shear flow. Under some assumptions we prove that such solutions exist at least for propagation speeds c {\in}]c*,…

Analysis of PDEs · Mathematics 2014-12-19 Léonard Monsaingeon , Alexeï Novikov , Jean-Michel Roquejoffre
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