Researcher, Dept. Mathematics and Applied Informatic (MIA).



INRA - Unité de Biostatistiques et Processus Spatiaux (UR546)
Domaine St-Paul - Site Agroparc
84914 Avignon Cedex

Tél.: +33 4 32 72 21 69
Fax: +33 4 32 72 21 82



Habilitation à Diricher les Recherches (HDR) since 2015

INRA Senior Researcher (CR1) since 2012
INRA Researcher (CR2) since 2008
Researcher in the Max Planck Institute for Mathematics in the Sciences (2006-2008)
Post-doc Ecos/Conycit Universidad de Chile/CMM UMI CNRS 2807 (2005-2006)
ATER Reseacher at the Laboratory Jacques-Louis Lions (University Paris 6) and at the Laboratory Ceremade (University Paris Dauphine) (2003-2005).
Cooperation, TMR "Front singularities and PDE" " Mathematical problem arising in sub and supersonic combustion media." Tel Aviv University, Israel (2000-2002)
PhD Student, in the Laboratoire Jacques-Louis Lions (formerly Laboratoire d'Analyse Numérique), University Paris 6 (1999-2003).



A biological invasion is characterized by an area's growth of repartition of a species per a given period of time. Whether natural or artificial, biological invasions play an important role in the evolution of species. However, the changes induced by these invasions may have devastating consequences. The introduction of new species (animal or plant) represents a significant perturbation of the native population, creating a major threat for most of the endemic species in the ecosystem.
One of the prime objectives of mathematical modeling in ecology is to provide a simple and efficient way to describe, understand and predict the results of such invasions.
From this perspective, my research effort essentially focuses on the following topics :

          o Modeling the dispersal of individuals and impact of space heterogeneity

          o Speed of invasion and characterization of the phase transition

          o  Impact of space heterogeneity on the survival of individuals

          o  Dynamic demo-genetic  (epidemiologie, QTL, ...)


          o Non local Equations applied to ecology and virology.
          o Heterogeneous dispersal via integro-differential operators.
          o PDE's system in combustion theory.
          o Equation with random coeficient/ System of SPDE.


     Habilitation à Diriger les Recherches (2015):

        Contribution à l'étude d'équations non locales en dynamique des populations
      Mémoire d'HDR, soutenue le 16 Novembre 2015https://tel.archives-ouvertes.fr/tel-01238013/document.

     Phd Thesis (2003):

      Equation de réaction diffusion non-locale
    Thèse de doctorat, soutenue le 18 Novembre 2003. https://tel.archives-ouvertes.fr/tel-00004313/document


Articles publiés:

Concentration Phenomenon in Some Non-Local Equation (Bonnefon, Coville, Legendre) To appear in DCDS-B.   http://arxiv.org/pdf/1510.01971v1

On eigenvalue problems arising from nonlocal diffusion models     (Coville, Li, Wang ) To appear in DCDS-A.

Persistence criteria for populations with non-local dispersion   (Berestycki, Coville, Vo) To appear in JOMB http://arxiv.org/pdf/1406.6346v2

Nonlocal refuge model with a partial control   DCDS-A 2015   http://arxiv.org/abs/1305.7122

Inside dynamics of solutions of integro-differential equations (Bonnefon, Coville, Garnier, Roques) DCDS-B 2015

Bistable travelling waves for nonlocal reaction diffusion equations (Alfaro, Coville, Raoul), DCDS-A 2014    http://fr.arxiv.org/abs/1303.3554

Singular measure as principal eigenfunction of some nonlocal operators, Applied Mathematical Letter 2013   http://fr.arxiv.org/abs/1302.0949

Traveling waves in a nonlocal equation as a model for a population structured by a space variable and a phenotypical trait (Alfaro, Coville, Raoul ) Communication in PDE 2013  http://fr.arxiv.org/abs/1211.3228

Rapid travelling waves in the nonlocal Fisher equation connect two unstable states (Alfaro, Coville) Applied Mathematical Letters 2012, http://fr.arxiv.org/abs/1205.2349

Modelling the evolutionary dynamics of viruses within their hosts : a case study using high-throughput sequencing (Coville, Fabre, Montarry, Senoussi, Simon, Moury) PloS Pathogen 2012, http://www.plospathogens.org/article/info%3Adoi%2F10.1371%2Fjournal.ppat.1002654

Pulsating wave arising in a nonlinear non local problem (avec J. Davila et S. Martinez) Annale de l'IHP/ Analyse nonlinéaire 2012. http://fr.arxiv.org/abs/1302.1053

Patchy patterns due to group dispersal   (avec Fayard, Roques, Soubeyrand) Journal of Theoretical Biology 271 (2011).

Harnack type inequality for positive solution of some integral equation  Ann. Mat. Pura e Appl. (2011) http://fr.arxiv.org/abs/1302.1677

Existence of multiple of ?ame balls in a thermo-diffusive combustion model with heat loss (Coville, Davila) DCDS  B, Vol. 16, No 3, (2011) http://fr.arxiv.org/abs/1106.5597

Non-existence of positive stationary solutions for a class of semilinear Pde's with random coefficients (Coville, Dirr, Luckhaus) NHM Volume 5, Number 4, (2010), http://fr.arxiv.org/abs/1106.5138

On the principal eigenvalue of some inhomogeneous nonlocal operator in general domains  (Coville) J. Differential Equations, Vol 249, 2921-2953 (2010), http://fr.arxiv.org/abs/1106.5137

Remarks on the strong maximum principle for nonlocal operators (Coville) Electron. J. Differential Equations (2008), No. 66., http://ejde.math.txstate.edu/Volumes/2008/66/abstr.html

 Nonlocal anisotropic dispersal with monostable nonlinearity (Coville, Davila , Martinez) J. Differential Equations 244 (2008), no. 12, 3080-3118. http://fr.arxiv.org/abs/1106.4531

Existence/Non-existence and uniqueness of solutions to a non-local equation with monostable nonlinearity (Coville, Davila, Martinez) SIAM Journal on Mathematical Analysis, 39 (2008), no 5, 1693?1709.http://fr.arxiv.org/abs/1106.5135

Travelling fronts in asymmetric nonlocal reaction diffusion equation : The bistable and ignition case (Coville) Prépublication du CMM, Hal-00696208, http://hal.archives-ouvertes.fr/index.php?action_todo=search&view_this_doc=hal-00696208&version=1&halsid=ngfvlf0sblu5tbe17mcp0e5qi4

Maximum principle, slidings techniques and applications to nonlocal equations (Coville) Electronic Journal of Differential Equations, Vol. (2007), No. 68, pp. 1-23. http://ejde.math.txstate.edu/Volumes/2007/68/abstr.html

A nonlocal inhomogenous dispersal process ( Coville, Cortazar, Elgueta, Mart?nez) J. Differential Equation 241 (2007), no 2, 332?358.

On a non-local reaction diffusion equation arising in population dynamics (Coville, Dupaigne) Proc. Math. Roy. Soc. of Edinburgh Sect. A 137 (2007), no 4.

On uniqueness and monotonicity of solutions of non-local reaction diffusion equations (Coville) Ann. Mat. Pura e Appl. (4) 185 (2006), no. 3.

Propagation speed of travelling fronts in non-local reaction diffusion equations (Coville, Dupaigne) Nonlinear Anal. 60 (2005), no. 5.

Travelling fronts in integro-differential equations (Coville, Dupaigne) C.R. Acad. Sci. Paris S?r I. 337 (2003) 25-30.

Monotonicity in integro-differential equations  (Coville) C.R. Acad. Sci. Paris S?r I. 337 (2003) 445-450.


Articles soumis:

Convergence to the equilibrium in a Lotka-Volterra ode competition system with mutation (Coville, Fabre) http://fr.arxiv.org/abs/1301.6237

Estimating the dispersal of an epidemie in corridor (Xhaard, Soubeyrand, Coville, Fabre, Halkett)

Convergence to the equilibrium of positive solution of some  mutation-selection model http://arxiv.org/abs/1308.6471

On the definition and scaling properties of the principal eigenvalue of some nonlocal operator (Berestycki, Coville, Vo) https://hal.archives-ouvertes.fr/hal-01245634

En Préparation:

Remarks on modelling dispersal with general nonlocal operators  (Coville,Martinez)