Related papers: Heteroclinic Travelling Waves of Gradient Diffusio…
We study the existence of traveling waves for the parabolic system \begin{equation} \partial_t w - \partial_{x}^2 w = -\nabla_{\mathbb{u}} W(w) \mbox{ in } [0,+\infty) \times \mathbb{R} \end{equation} where $W$ is a potential bounded below…
n this paper we show the existence of traveling waves $w: [0,+\infty) \times \mathbb{R}^2 \to \mathbb{R}^k$ ($k \geq 2$) for the parabolic Allen-Cahn system \begin{equation} \partial_t w - \Delta w = -\nabla_u V(w) \mbox{ in } [0,+\infty)…
We consider the equation $u_t=u_{xx}+b(x)u(1-u),$ $x\in\mathbb R,$ where $b(x)$ is a nonnegative measure on $\mathbb R$ that is periodic in $x.$ In the case where $b(x)$ is a smooth periodic function, it is known that there exists a…
We study travelling waves on a two--dimensional lattice with linear and nonlinear coupling between nearest particles and a periodic nonlinear substrate potential. Such a discrete system can model molecules adsorbed on a substrate crystal…
We are concerned with the asymptotic behaviour of classical solutions of systems of the form u_t = Au_xx + f(u, u_x), x in R, t>0, u(x,t) a vector in RN, with u(x,0)= U(x), where A is a positive-definite diagonal matrix and f is a…
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…
Let $W:R^m\rightarrow R$ be a nonnegative potential with exactly two nondegenerate zeros $a_-\neq a_+\in R^m$. We assume that there are$ N\geq 1$ distinct heteroclinic orbits connecting $a_-$ to $a_+$ represented by maps $ u_1,\ldots,u_N$…
This paper is concerned with a lattice dynamical system modeling the evolution of susceptible and infective individuals at discrete niches. We prove the existence of traveling waves connecting the disease-free state to non-trivial leftover…
In this paper, a ratio-dependent Holling-Tanner system with nonlocal diffusion is taken into account, where the prey is subject to a strong Allee effect. To be special, by applying Schauder's fixed point theorem and iterative technique, we…
We consider the quartic focusing Half Wave equation (HW) in one space dimension. We show first that that there exist traveling wave solutions with arbitrary small $H^{\frac 12}(\R)$ norm. This fact shows that small data scattering is not…
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…
The present paper deals with the following hyperbolic--elliptic coupled system, modelling dynamics of a gas in presence of radiation, $u_{t}+ f(u)_{x} +Lq_{x}=0, -q_{xx} + Rq +G\cdot u_{x}=0,$ where $u\in\R^{n}$, $q\in\R$ and $R>0$, $G$,…
This paper is concerned with the traveling wave solutions for integro-difference systems of higher order. By using Schauder fixed point theorem, the existence of traveling wave solutions is reduced to the existence of generalized upper and…
We report experimental observations of traveling waves in a pure fluid with a free surface situated in a long container submitted to a horizontal temperature gradient perpendicular to its large extension. Above a critical value of the…
In this note we consider the action functional \[ \int_{\mathbb{R} \times \omega} \left( 1 - \sqrt{ 1 - |\nabla u|^2 } + W(u) \right) \, \mathrm{d}t, \] where $W$ is a double well potential and $\omega$ is a bounded domain of…
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…
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,…
For nonlinear parabolic systems of the form \[ \partial_t w(x,t) = \partial_{x}^2 w(x,t) - \nabla V\bigl(w(x,t)\bigr) \,, \] the following conclusions are proved to hold generically with respect to the potential $V$: every travelling front…
We study traveling wave solutions of an equation for surface waves of moderate amplitude arising as a shallow water approximation of the Euler equations for inviscid, incompressible and homogenous fluids. We obtain solitary waves of…
We develop the theory of transportation and localization of a transparent dielectric spherical particle with the gradient forces in the interference field of orthogonally directed standing laser waves $E_z (\cos kz)$ and $E_x (\cos kx)$. It…