35 research outputs found
Pushed traveling fronts in monostable equations with monotone delayed reaction
We study the existence and uniqueness of wavefronts to the scalar
reaction-diffusion equations with monotone delayed reaction term and . We are mostly interested in the situation when the graph of is not
dominated by its tangent line at zero, i.e. when the condition , is not satisfied. It is well known that, in such a case, a
special type of rapidly decreasing wavefronts (pushed fronts) can appear in
non-delayed equations (i.e. with ). One of our main goals here is to
establish a similar result for . We prove the existence of the minimal
speed of propagation, the uniqueness of wavefronts (up to a translation) and
describe their asymptotics at . We also present a new uniqueness
result for a class of nonlocal lattice equations.Comment: 17 pages, submitte
Travelling wavefronts in nonlocal diffusion equations with nonlocal delay effects
This paper deals with the existence, monotonicity, uniqueness and asymptotic
behaviour of travelling wavefronts for a class of temporally delayed, spatially
nonlocal diffusion equations
Positive Stationary Solutions and Spreading Speeds of KPP Equations in Locally Spatially Inhomogeneous Media
The current paper is concerned with positive stationary solutions and spatial
spreading speeds of KPP type evolution equations with random or nonlocal or
discrete dispersal in locally spatially inhomogeneous media. It is shown that
such an equation has a unique globally stable positive stationary solution and
has a spreading speed in every direction. Moreover, it is shown that the
localized spatial inhomogeneity of the medium neither slows down nor speeds up
the spatial spreading in all the directions
Traveling waves for a model of the Belousov-Zhabotinsky reaction
Following J.D. Murray, we consider a system of two differential equations
that models traveling fronts in the Noyes-Field theory of the
Belousov-Zhabotinsky (BZ) chemical reaction. We are also interested in the
situation when the system incorporates a delay . As we show, the BZ
system has a dual character: it is monostable when its key parameter and it is bistable when . For , and for each
admissible wave speed, we prove the uniqueness of monotone wavefronts. Next, a
concept of regular super-solutions is introduced as a main tool for generating
new comparison solutions for the BZ system. This allows to improve all
previously known upper estimations for the minimal speed of propagation in the
BZ system, independently whether it is monostable, bistable, delayed or not.
Special attention is given to the critical case which to some extent
resembles to the Zeldovich equation.Comment: 23 pages, to appear in the Journal of Differential Equation
Recent developments on wave propagation in 2-species competition systems
[[abstract]]In this paper, we shall survey some recent results on the wave propagation in 2-species competition systems with Lotka-Volterra type non- linearity. This includes systems with continuous and discrete diffusion (or migration). We are interested in both monostable case and bistable with strong competition case. Questions on minimal speed for the monostable case, uniqueness of wave speed and propagation failure in the bistable case, monotonicity and uniqueness of wave profile for both cases are addressed. Finally, we give some open problems on wave propagation in 2-species competition systems.[[journaltype]]國外[[incitationindex]]SCI[[ispeerreviewed]]Y[[booktype]]紙本[[booktype]]電子版[[countrycodes]]US
Traveling Wavefronts in an Antidiffusion Lattice Nagumo Model
This is the published version, also available here: http://dx.doi.org/10.1137/100819461.We consider a system of lattice Nagumo equations with cubic nonlinearity, but with a negative discrete diffusion coefficient. We are interested in the existence, uniqueness, stability, and nonexistence of the traveling wavefront solutions of this system, and we shall call this problem the antidiffusion lattice Nagumo problem. By rewriting this system as a spatially periodic system with inhomogeneous but positive periodic diffusion coefficients and periodic nonlinearities, we uncover a rich solution behavior that includes many possible connecting orbits in the antidiffusion case. Second, we observe the presence of bistable and monostable dynamics. In the bistable region, we study the phenomenon of propagation of failure while in the monostable region, we compute the minimum wave speed