Results 51 to 60 of about 319 (78)

Generalized transition waves and their properties [PDF]

arXiv, 2010
In this paper, we generalize the usual notions of waves, fronts and propagation speeds in a very general setting. These new notions, which cover all classical situations, involve uniform limits, with respect to the geodesic distance, to a family of hypersurfaces which are parametrized by time.
arxiv  

Travelling waves with continuous profile for hyperbolic Keller-Segel equation

European Journal of Applied Mathematics
This work describes a hyperbolic model for cell-cell repulsion with population dynamics. We consider the pressure produced by a population of cells to describe their motion.
Quentin Griette, Pierre Magal, Min Zhao
doaj   +1 more source

Global exponential convergence to variational traveling waves in cylinders [PDF]

SIAM J. Math. Anal. 44, 293--315 (2012), 2011
We prove, under generic assumptions, that the special variational traveling wave that minimizes the exponentially weighted Ginzburg-Landau functional associated with scalar reaction-diffusion equations in infinite cylinders is the long-time attractor for the solutions of the initial value problems with front-like initial data.
arxiv  

The evolution problem for the 1D nonlocal Fisher-KPP equation with a top hat kernel. Part 1. The Cauchy problem on the real line

European Journal of Applied Mathematics
We study the Cauchy problem on the real line for the nonlocal Fisher-KPP equation in one spatial dimension, \begin{equation*} u_t = D u_{xx} + u(1-\phi *u), \end{equation*} where $\phi *u$ is a spatial convolution with the top hat kernel,
David John Needham, John Billingham, Nikolaos Michael Ladas, John Meyer   +3 more
doaj   +1 more source

Explicit upper and lower bounds for the traveling wave solutions of Fisher-Kolmogorov type equations [PDF]

arXiv, 2011
It is well-known that the existence of traveling wave solutions for reaction-diffusion partial differential equations can be proved by showing the existence of certain heteroclinic orbits for related autonomous planar differential equations. We introduce a method for finding explicit upper and lower bounds of these heteroclinic orbits.
arxiv  

Travelling wavefronts for the Belousov–Zhabotinsky system with non-local delayed interaction

European Journal of Applied Mathematics
This article offers an advanced and novel investigation into the intricate propagation dynamics of the Belousov–Zhabotinsky system with non-local delayed interaction, which exhibits dynamical transition structure from bistable to monostable.
Yuanxi Yue, Chunhua Ou
doaj   +1 more source

Traveling waves of an FKPP-type model for self-organized growth. [PDF]

J Math Biol, 2022
Kreten F.
europepmc   +1 more source

Derivation and travelling wave analysis of phenotype-structured haptotaxis models of cancer invasion

European Journal of Applied Mathematics
We formulate haptotaxis models of cancer invasion wherein the infiltrating cancer cells can occupy a spectrum of states in phenotype space, ranging from ‘fully mesenchymal’ to ‘fully epithelial’. The more mesenchymal cells are those that display stronger
Tommaso Lorenzi, Fiona R. Macfarlane, Kevin J. Painter   +2 more
doaj   +1 more source

Rarefaction pulses for the Nonlinear Schrodinger Equation in the transonic limit [PDF]

arXiv, 2012
We investigate the properties of finite energy travelling waves to the nonlinear Schrodinger equation with nonzero conditions at infinity for a wide class of nonlinearities. In space dimension two and three we prove that travelling waves converge in the transonic limit (up to rescaling) to ground states of the Kadomtsev-Petviashvili equation.
arxiv  

Traveling Waves in a Three Species Competition-cooperation System [PDF]

arXiv, 2013
This paper studies the traveling wave solutions to a three species competition cooperation system. The existence of the traveling waves is investigated via monotone iteration method. The upper and lower solutions come from either the waves of KPP equation or those of certain Lotka Volterra system.
arxiv