English
Related papers

Related papers: Travelling wave solutions in a negative nonlinear …

200 papers

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 consider a nonlocal reaction-diffusion equation as a model for a population structured by a space variable and a phenotypical trait. To sustain the possibility of invasion in the case where an underlying principal eigenvalue is negative,…

Analysis of PDEs · Mathematics 2012-12-03 Matthieu Alfaro , Jérôme Coville , Gaël Raoul

We study the existence of monotone traveling wave solutions in a class of nonclassical diffusion equations that include both standard diffusion and a higher-order mixed space-time dispersive term. The reaction term is nonlinear and subject…

Analysis of PDEs · Mathematics 2025-10-28 William Barker , Le Xuan Dong , Vu Trong Luong , Nguyen Duong Toan

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

Sufficient conditions for either existence or non-existence of traveling wave solutions for a general quasi-linear reaction-diffusion-convection equation, possibly highly degenerate or singular, with discontinuous coefficients are…

Analysis of PDEs · Mathematics 2025-07-09 Umberto Guarnotta , Cristina Marcelli

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

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

In this paper, we study the existence of traveling wave solutions and the spreading speed for the solutions of an age-structured epidemic model with nonlocal diffusion. Our proofs make use of the comparison principles both to construct…

Analysis of PDEs · Mathematics 2024-05-24 Arnaud Ducrot , Hao Kang

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

We consider an epidemic model with direct transmission given by a system of nonlinear partial differential equations and study the existence of traveling wave solutions. When the basic reproductive number of the considered model is less…

Analysis of PDEs · Mathematics 2019-10-08 Dawit Denu , Sedar Ngoma , Rachidi B. Salako

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

In this note, we investigate a doubly nonlinear diffusion equation in the slow diffusion regime. We prove stability of the pressure of solutions that are close to traveling wave solutions in a homogeneous Lipschitz sense. We derive…

Analysis of PDEs · Mathematics 2026-02-25 Christian Seis , Dominik Winkler

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

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

We study two systems of reaction diffusion equations with monostable or bistable type of nonlinearity and with free boundaries. These systems are used as multi-species competitive model. For two-species models, we prove the existence of a…

Analysis of PDEs · Mathematics 2013-07-23 Jian Yang , Bendong Lou

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

This paper is concerned with the existence and the stability of travelling wave solutions to a bistable reaction-diffusion equation with a jump discontinuious point on nonlinear term. Sub-super solution method is used throughout this paper.…

Analysis of PDEs · Mathematics 2022-06-07 Lingling Hou

We look for traveling wave solutions to the nonlinear Schr\"odinger equation with a subsonic speed, covering several physical models with Sobolev subcritical nonlinear effects. Our approach is based on a variant of Sobolev-type inequality…

Analysis of PDEs · Mathematics 2025-07-31 Laura Baldelli , Bartosz Bieganowski , Jarosław Mederski

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
‹ Prev 1 2 3 10 Next ›