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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

Lucas and Moll have proposed a system of forward-backward partial differential equations that model knowledge diffusion and economic growth. It arises from a microscopic model of learning for a mean-field type interacting system of…

Analysis of PDEs · Mathematics 2021-09-22 George Papanicolaou , Lenya Ryzhik , Katerina Velcheva

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

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

In this paper, we provide a sufficient condition on successful invasion by the predator. Specially, we obtain the persistence of traveling wave solutions of predator-prey system, in which the predator can survive without the predation of…

Analysis of PDEs · Mathematics 2023-06-02 Hongliang Li , Min Zhao , Rong Yuan

Using an abstract scheme of monotone semiflows, the existence of bistable traveling wave solutions of a competitive recursion system with Ricker nonlinearity is established. The traveling wave solutions formulate the strong inter-specific…

Dynamical Systems · Mathematics 2013-02-06 Shuxia Pan , Jie Liu

This paper is concerned with the existence of traveling wave solutions for diffusive two-species Lotka-Volterra systems with delay in both the reaction and diffusion terms without monotonicity. We extend the partial or cross monotone…

Analysis of PDEs · Mathematics 2023-03-21 William Barker

The existence of traveling front solutions to bistable lattice differential equations in the absence of a comparison principle is studied. The results are in the spirit of those in Bates, Chen, and Chmaj in[1], but are applicable to vector…

Dynamical Systems · Mathematics 2013-10-08 Erik S. Van Vleck , Aijun Zhang

We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…

Pattern Formation and Solitons · Physics 2013-05-29 V. N. Biktashev , M. A. Tsyganov

The present paper is concerned with the existence of traveling wave solutions of the asymptotic model, derived by the authors in a previous work, to approximate the unidirectional evolution of a collision-free plasma in a magnetic field.…

Analysis of PDEs · Mathematics 2024-10-14 Diego Alonso-Orán , Angel Durán , Rafael Granero-Belinchón

We study two mathematical descriptions of a charged particle interacting with it's self-generated electromagnetic field. The first model is the one-body Maxwell-Schr\"odinger system where the interaction of the spin with the magnetic field…

Mathematical Physics · Physics 2014-02-18 Kim Petersen , Jan Philip Solovej

A thorough analysis is performed to find traveling waves in a qualitative reaction-diffusion system inspired by a predator-prey model. We provide rigorous results coming from a standard local stability analysis, numerical bifurcation…

Chaotic Dynamics · Physics 2022-11-09 Edgardo Villar-Sepúlveda , Pablo Aguirre , Víctor F. Breña-Medina

We analyze the weak solution concept for the Fornberg-Whitham equation in case of traveling waves with a piecewise smooth profile function. The existence of discontinuous weak traveling wave solutions is shown by means of analysis of a…

Analysis of PDEs · Mathematics 2018-04-23 Guenther Hoermann

This paper is devoted to study the wave propagation and its stability for a class of two-component discrete diffusive systems. We first establish the existence of positive monotone monostable traveling wave fronts. Then, applying the…

Dynamical Systems · Mathematics 2020-12-02 Zhixian Yu , Yuji Wan , Cheng-Hsiung Hsu

We study an incompressible Darcy's free boundary problem, recently introduced in [22]. Our goal is to prove the existence of non-trivial traveling wave solutions and thus validate the interest of this model to describe cell motility. The…

Analysis of PDEs · Mathematics 2022-05-10 Thomas Alazard , Martina Magliocca , Nicolas Meunier

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 pattern formation in a class of reaction-advection-diffusion systems modeling the population dynamics of two predators and one prey. We consider the biological situation that both predators forage along the population…

Analysis of PDEs · Mathematics 2016-10-26 Ke Wang , Qi Wang , Feng Yu

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

We consider a model of the predator--prey community with prey-taxis. By that we mean the capability of the predators to get moving in a certain direction on the macroscopic level in response to the prey density gradients. Additionally, we…

Analysis of PDEs · Mathematics 2025-09-03 Andrey Morgulis , Karrar Malal

In this paper, we investigate so-called forced wave solutions of a three components reaction-diffusion system from population dynamics. Our system involves three species that are respectively two competing preys and one predator; moreover,…

Analysis of PDEs · Mathematics 2022-12-12 Thomas Giletti , Jong-Shenq Guo