Related papers: Traveling waves in reaction-diffusion-convection e…
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…
In this paper we prove the existence of finite traveling-wave type solutions to the nonlinear double degenerate parabolic equation of turbulent filtration with absorption.
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…
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…
We examine travelling wave solutions of the reaction-diffusion equation, $\partial_t u= R(u) + \partial_x \left[D(u) \partial_x u\right]$, with a Stefan-like condition at the edge of the moving front. With only a few assumptions on $R(u)$…
We consider general reaction diffusion systems posed on rectangular lattices in two or more spatial dimensions. We show that travelling wave solutions to such systems that propagate in rational directions are nonlinearly stable under small…
We investigate the presence of soliton solutions in some classes of nonlinear partial differential equations, namely generalized Korteweg-de Vries-Burgers, Korteveg-de Vries-Huxley, and Korteveg-de Vries-Burgers-Huxley equations, which…
We investigate in this paper a scalar reaction diffusion equation with a nonlinear reaction term depending on x-ct. Here, c is a prescribed parameter modelling the speed of climate change and we wonder whether a population will survive or…
The traveling waves for surface diffusion of plane curves are studied. We consider an evolving plane curve with two endpoints, which can move freely on the x-axis with generating constant contact angles. For the evolution of this plane…
This paper reports results on the classification of traveling wave solutions, including nonnegative weak sense, in the spatial 1D degenerate parabolic equation. These are obtained through dynamical systems theory and geometric approaches…
We consider a free boundary model of epithelial cell migration with logistic growth and nonlinear diffusion induced by mechanical interactions. Using numerical simulations, phase plane and perturbation analysis, we find and analyse…
An analysis of traveling wave solutions of pure cross-diffusion systems, i.e., systems that lack reaction and self-diffusion terms, is presented. Using the qualitative theory of phase plane analysis the conditions for existence of different…
We study traveling waves for a reaction-diffusion equation with nonlocal anisotropic diffusion and a linear combination of local and nonlocal monostable-type reactions. We describe relations between speeds and asymptotic of profiles of…
We consider a reaction-diffusion equation with a convection term in one space variable, where the diffusion changes sign from the positive to the negative and the reaction term is bistable. We study the existence of wavefront solutions,…
In this paper we study the existence of traveling wave solutions for a free-boundary problem modeling the phase transition of a material where the heat is transported by both conduction and radiation. Specifically, we consider a…
This article produces wave equations and constructs traveling wave solutions that are intimately related to Newton's equations of celestial mechanics. The traveling wave solutions are expressed in ``closed form'' in terms of elementary…
We prove the existence and uniqueness of a family of travelling waves in a degenerate (or singular) quasilinear parabolic problem that may be regarded as a generalization of the semilinear Fisher-Kolmogorov-Petrovski-Piscounov equation for…
We consider reaction-diffusion equations and Korteweg-de Vries-Burgers (KdVB) equations, i.e. scalar conservation laws with diffusive-dispersive regularization. We review the existence of traveling wave solutions for these two classes of…
We present in closed form some special travelling-wave solutions (on the real line or on the circle) of a perturbed sine-Gordon equation. The perturbation of the equation consists of a constant forcing term $\gamma$ and a linear dissipative…
Many reaction-diffusion models produce travelling wave solutions that can be interpreted as waves of invasion in biological scenarios such as wound healing or tumour growth. These partial differential equation models have since been adapted…