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Journal of Differential Equations | 2008

Nonlocal anisotropic dispersal with monostable nonlinearity

Jérôme Coville; Juan Dávila; Salomé Martínez

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.


Journal of Differential Equations | 2010

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

Jérôme Coville

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.


Siam Journal on Mathematical Analysis | 2008

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

Jérôme Coville; Juan Dávila; Salomé Martínez

Let


Annales De L Institut Henri Poincare-analyse Non Lineaire | 2013

Pulsating fronts for nonlocal dispersion and KPP nonlinearity

Jérôme Coville; Juan Dávila; Salomé Martínez

J \in C(\mathbb{R})


Communications in Partial Differential Equations | 2013

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

Matthieu Alfaro; Jérôme Coville; Gaël Raoul

,


PLOS Pathogens | 2012

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

Frédéric Fabre; Josselin Montarry; Jérôme Coville; Rachid Senoussi; Vincent Simon; Benoît Moury

J\ge 0


Annali di Matematica Pura ed Applicata | 2012

Harnack type inequality for positive solution of some integral equation

Jérôme Coville

,


Journal of Theoretical Biology | 2011

Patchy patterns due to group dispersal

Samuel Soubeyrand; Lionel Roques; Jérôme Coville; Julien Fayard

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


Annali di Matematica Pura ed Applicata | 2006

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

Jérôme Coville

and consider the nonlocal diffusion operator


Journal of Differential Equations | 2007

A nonlocal inhomogeneous dispersal process

Carmen Cortázar; Jérôme Coville; Manuel Elgueta; Salomé Martínez

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

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