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This paper is concerned with the traveling wave solutions of an integro-difference competition system, of which the purpose is to model the coinvasion-coexistence process of two competitors with age structure. The existence of nontrivial…

Dynamical Systems · Mathematics 2013-10-31 Shuxia Pan , Guo Lin

We prove the existence of a continuous family of positive and generally non-monotone travelling fronts in delayed reaction-diffusion equations $u_t(t,x) = \Delta u(t,x)- u(t,x) + g(u(t-h,x)) (*)$, when $g \in C^2(R_+,R_+)$ has exactly two…

Dynamical Systems · Mathematics 2013-03-04 Teresa Faria , Sergei Trofimchuk

We study the existence and nonexistence of traveling waves of general diffusive Kermack-McKendrick SIR models with standard incidence where the total population is not constant. The three classes, susceptible $S$, infected $I$ and removed…

Analysis of PDEs · Mathematics 2014-02-18 Haiyan Wang , Xiang-Sheng Wang

This paper is concerned with the asymptotic spreading behavior of solutions of the Lotka-Volterra system with strong competition in $\mathbb{R}^{N}$. Two types of initial conditions are proposed: (C1) two species initially occupy bounded…

Analysis of PDEs · Mathematics 2024-11-22 Hui Bao , Hongjun Guo

In this paper, we study three two competing species Lotka-Volterra competition models on finite connected graphs, with Dirichlet, Neumann or no boundary conditions. We get that when time goes to infinity, either one specie extincts while…

Analysis of PDEs · Mathematics 2022-10-26 Yuanyang Hu , Chengxia Lei

In this paper we study the invasion fronts of spatially periodic monotone reaction-diffusion systems in a multi-dimensional setting. We study the pulsating traveling waves that connect the trivial equilibrium, for which all components of…

Analysis of PDEs · Mathematics 2025-11-14 Liangliang Deng , Arnaud Ducrot , Quentin Griette

The paper is concerned with a singular limit for the bistable traveling wave problem in a very large class of two-species fully nonlinear parabolic systems with competitive reaction terms. Assuming existence of traveling waves and enough…

Analysis of PDEs · Mathematics 2021-12-15 Léo Girardin , Danielle Hilhorst

In this work we revisit the existence, stability and dynamics of unstable traveling solitary waves in the context of lattice dynamical systems. We consider a nonlinear lattice of an $\alpha$-Fermi-Pasta-Ulam type with the additional feature…

Pattern Formation and Solitons · Physics 2021-03-16 H. Duran , H. Xu , P. G. Kevrekidis , A. Vainchtein

We investigate the existence and properties of traveling waves for the Euler-Korteweg system with general capillarity and pressure. Our main result is the existence in dimension two of waves with arbitrarily small energy. They are obtained…

Analysis of PDEs · Mathematics 2017-09-13 Corentin Audiard

This paper deals with the existence of travelling wave solutions for a general one-dimensional nonlinear Schr\"odinger equation. We construct these solutions by minimizing the energy under the constraint of fixed momentum. We also prove…

Analysis of PDEs · Mathematics 2024-04-10 Jordan Berthoumieu

We study traveling wave solutions of the nonlinear variational wave equation. In particular, we show how to obtain global, bounded, weak traveling wave solutions from local, classical ones. The resulting waves consist of monotone and…

Analysis of PDEs · Mathematics 2022-01-13 Katrin Grunert , Audun Reigstad

In this study, we investigate the existence of traveling wave solutions for a SIR model on two-dimensional lattice. The existence of traveling waves is established within the framework of upper and lower solutions and the Schauder…

Dynamical Systems · Mathematics 2026-02-19 Ran Zhang , Shunchang Su , Xue Ren

We study the traveling wave solutions to a reaction diffusion system modeling the public goods game with altruistic behaviors. The existence of the waves is derived through monotone iteration of a pair of classical upper- and lower…

Analysis of PDEs · Mathematics 2009-09-09 Xiaojie Hou , Wei Feng

This paper is devoted to the study of propagation phenomena for a Lotka-Volterra reaction-advection-diffusion competition model in a periodic habitat. We first investigate the global attractivity of a semi-trival steady state for the…

Analysis of PDEs · Mathematics 2014-10-20 Xiao Yu , Xiao-Qiang Zhao

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 Fisher-KPP-type equation, where both diffusion and nonlinear part are nonlocal, with anisotropic probability kernels. Under minimal conditions on the coefficients, we prove existence, uniqueness, and uniform space-time…

Analysis of PDEs · Mathematics 2015-09-22 Dmitri Finkelshtein , Yuri Kondratiev , Pasha Tkachov

In this paper we are investigating the long time behaviour of the solution of a mutation competition model of Lotka-Volterra's type. Our main motivation comes from the analysis of the Lotka-Volterra's competition system with mutation which…

Analysis of PDEs · Mathematics 2013-03-08 Jerome Coville , Frederic Fabre

We prove the existence of nontrivial finite energy traveling waves for a large class of nonlinear Schr\"odinger equations with nonzero conditions at infinity (includindg the Gross-Pitaevskii and the so-called "cubic-quintic" equations) in…

Analysis of PDEs · Mathematics 2017-06-06 David Chiron , Mihai Mariş

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

This paper is concerned with some spreading properties of monostable Lotka--Volterra two-species competition--diffusion systems when the initial values are null or exponentially decaying in a right half-line. Thanks to a careful…

Analysis of PDEs · Mathematics 2019-06-19 Léo Girardin , King-Yeung Lam