Non-Local dispersal and bistability

Non-Local Dispersal and Bistability

The scalar initial value problem ut = ρDu+ f(u), is a model for dispersal. Here u represents the density at point x of a compact spatial region Ω ∈ R and time t, and u(·) is a function of t with values in some function space B. D is a bounded linear operator and f(u) is a bistable nonlinearity for the associated ODE ut = f(u). Problems of this type arise in mathematical ecology and materials sc...

Random Dispersal vs Non-Local Dispersal

Random dispersal is essentially a local behavior which describes the movement of organisms between adjacent spatial locations. However, the movements and interactions of some organisms can occur between non-adjacent spatial locations. To address the question about which dispersal strategy can convey some competitive advantage, we consider a mathematical model consisting of one reaction-diffusio...

Non–Autonomous Non–Local Dispersal - Spectral Theory

In applications to spatial structure in biology and to the theory of phase transition, it has proved useful to generalize the idea of diffusion to a non-local dispersal with an integral operator replacing the Laplacian. We study the spectral problem for the linear scalar equation ut(x, t) = ∫ Ω K(x, y)u(y, t)dy+ h(x, t)u(x, t), and tackle the extra technical difficulties arising because of the ...

Non-local Anisotropic Dispersal with Monostable Nonlinearity

We study the travelling wave problem J ⋆ u− u− cu + f(u) = 0 in R, u(−∞) = 0, u(+∞) = 1 with an asymmetric kernel J and a monostable nonlinearity. We prove the existence of a minimal speed, and under certain hypothesis the uniqueness of the profile for c 6= 0. For c = 0 we show examples of non-uniqueness.

A Non Local Inhomogeneous Dispersal Process