Related papers: Travelling wave solutions in a negative nonlinear …
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…
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…
We examine travelling wave solutions of the Porous-Fisher model, $\partial_t u(x,t)= u(x,t)\left[1-u(x,t)\right] + \partial_x \left[u(x,t) \partial_x u(x,t)\right]$, with a Stefan-like condition at the moving front, $x=L(t)$. Travelling…
Existence of non-negative weak solutions is shown for a full curvature thin-film model of a liquid thin film flowing down a vertical fibre. The proof is based on the application of a priori estimates derived for energy-entropy functionals.…
We study an integro-differential equation that describes the slow erosion of granular flow. The equation is a first order non-linear conservation law where the flux function includes an integral term. We show that there exist unique…
This paper deals with front propagation dynamics of monostable equations with nonlocal dispersal in spatially periodic habitats. In the authors' earlier works, it is shown that a general spatially periodic monostable equation with nonlocal…
In this paper we show that non-smooth functions which are distributional traveling wave solutions to the two component Camassa-Holm equation are distributional traveling wave solutions to the Camassa-Holm equation provided that the set…
In this article, we are interested in a non-monotone system of logistic reaction-diffusion equations. This system of equations models an epidemics where two types of pathogens are competing, and a mutation can change one type into the other…
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…
A nonlinear PDE featuring flux limitation effects together with those of the porous media equation (nonlinear Fokker-Planck) is presented in this paper. We analyze the balance of such diverse effects through the study of the existence and…
Planar wave trains are traveling wave solutions whose wave profiles are periodic in one spatial direction and constant in the transverse direction. In this paper, we investigate the stability of planar wave trains in reaction-diffusion…
We prove existence and uniqueness of travelling waves for a reaction-diffusion system coupling a classical reaction-diffusion equation in a strip with a diffusion equation on a line. To do this we use a continuation method which leads to…
We study the admissible values of the wave speed $c$ for which the beam equation with jumping nonlinearity possesses a travelling wave solution. In contrast to previously studied problems modelling suspension bridges, the presence of the…
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…
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 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…
This paper is devoted to the investigation of spatial spreading speeds and traveling wave solutions of monostable evolution equations with nonlocal dispersal in time and space periodic habitats. It has been shown in an earlier work by the…
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…
We consider reaction-diffusion equations that are stochastically forced by a small multiplicative noise term. We show that spectrally stable travelling wave solutions to the deterministic system retain their orbital stability if the…
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…