Jérôme Coville

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.

On a simple criterion for the existence of a principal eigenfunction of some nonlocal operators

Abstract In this paper we are interested in the existence of a principal eigenfunction of a nonlocal operator which appears in the description of various phenomena ranging from population dynamics to micro-magnetism. More precisely, we study the following eigenvalue problem: ∫ Ω J ( x − y g ( y ) ) ϕ ( y ) g n ( y ) d y + a ( x ) ϕ = ρ ϕ , where Ω ⊂ R n is an open connected set, J a non-negative kernel and g a positive function. First, we establish a criterion for the existence of a principal eigenpair ( λ p , ϕ p ) . We also explore the relation between the sign of the largest element of the spectrum with a strong maximum property satisfied by the operator. As an application of these results we construct and characterise the solutions of some nonlinear nonlocal reaction diffusion equations.

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})

Travelling Waves in a Nonlocal Reaction-Diffusion Equation as a Model for a Population Structured by a Space Variable and a Phenotypic Trait

,

Modelling the Evolutionary Dynamics of Viruses within Their Hosts: A Case Study Using High-Throughput Sequencing

J\ge 0

Harnack type inequality for positive solution of some integral equation

,

Patchy patterns due to group dispersal

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

On uniqueness and monotonicity of solutions of non-local reaction diffusion equation

and consider the nonlocal diffusion operator

A nonlocal inhomogeneous dispersal process

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