Salomé Martínez

Nonlocal anisotropic dispersal with monostable nonlinearity

Abstract We study the travelling wave problem J ⋆ u − u − c u ′ + 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 ≠ 0 . For c = 0 we show examples of nonuniqueness.

Existence and Uniqueness of Solutions to a Nonlocal Equation with Monostable Nonlinearity

Let

Pulsating fronts for nonlocal dispersion and KPP nonlinearity

J \in C(\mathbb{R})

Evolutionary stability of ideal free nonlocal dispersal.

,

The effect of diffusion for the multispecies Lotka-Volterra competition model

J\ge 0

Global bifurcation of solutions to diffusive logistic equations on bounded domains subject to nonlinear boundary conditions

,

Evolution of cross-diffusion and self-diffusion

\int_{\mbox{\tinyR}} J = 1

EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO SOME INHOMOGENEOUS NONLOCAL DIFFUSION PROBLEMS

and consider the nonlocal diffusion operator

High-frequency chaotic solutions for a slowly varying dynamical system

\mathcal{M}[u] = J \star u - u

Multi-clustered high-energy solutions for a phase transition problem

. We study the equation