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Luc
PAQUET

Mathematical analysis of the coupling between the radiative transfer equation and the heat conduction equation for a semi-transparent body submitted to the thermal radiations of a black radiative source. Optimal control of the absolute temperature inside the semi-transparent body by acting on the absolute temperature of the black radiative source. Optimal control of the deformation or of the stressfield of the semi-transparent body in the setting of the thermoviscoelasticity equations. 

Fonctions actuelles

    Dans le laboratoire

  • membre du jury de domaine
    organisation des CST (Comités de suivi de thèses)
    Director of the thesis of Hawraa Nabolsi (cotutelle with Pr. Ali Wehbe from the University of Lebanon); title of the thesis: "Contrôle Optimal des équations d'Evolution et ses Applications".
    Co-encadrant of the thesis of Tonia-Maria Alam.

Diplômes universitaires

  • 1978 :
    Doctorat d'Etat (15 décembre 1978, Université de l'Etat à Mons (Belgique))

Expériences professionnelles

  • 1.3.2017 au 31.8.2017 :
    Congé pour recherche (CRCT)

Valorisations academiques

    Responsabilités scientifiques de thèses

  • I have been the director of the thesis of El Sossa, R. Korikache, and I. Choubanne
    Actually director of the thesis of Hawraa Nabolsi in collaboration with Pr. Ali Wehbe from the University of Lebanon (cotutelle).
    Also, co-encadrant of the thesis of Tonia-Maria Alam.

    • Oeuvres

  • see the list of publications

    • Appartenance à des sociétés savantes

  • SMAI
    Reviewer for the "Mathematical Reviews"

Enseignements antérieurs

  • "Contrôle Optimal d'Equations aux Dérivées partielles", cours spécialisé du S4 en Master 2ème année Mathématiques, Université de Lille 1 (en coaccréditation avec l'UVHC, l'Université d'Artois et l'Université du Littoral Cote d'Opale) 

Éditeur

 R. Korikache, L. Paquet , "The completely discretized problem of the dual mixed formumlation for the heat diffusion equation in a polygonal domain by the Crank-Nicolson scheme in time", accepted for publication in SEMA-SIMAI Springer Series (2021). 

T.-M. Alam, L. Paquet, "Coupling the Heat equation with Maxwell’s equations", accepted for publication in "Journal of Mathematical Analysis and Its Applications" (JMAA), (27/6/ 2021). 

T.-M. Alam, S. Nicaise and L. Paquet, "An optimal control problem governed by the heat equation with nonconvex constraints applied to the selective laser melting process", Minimax Theory and its Applications, 6(2), 2021.

L. Paquet, R. Korikache, The complete discretization of the dual mixed method for the heat diffusion equation in a polygonal domain, Mathematics and Computers in Simulation, Available online 30 September 2020.

 H. Nabolsi, L. Paquet and Ali Wehbe, "Control of the Radiative Heating of a Semi-Transparent Body", Zeitschrift für angewandte Mathematik und Physik (ZAMP), First Online: 07 December 2018 at  https://doi.org/10.1007/s00033-018-1059-x, Volume 70, Issue 1, February 2019, Article 15.

L. Paquet, H. Nabolsi, "The Radiative Transfer Equation with a Nonhomogeneous Reflectivity Boundary Condition Coupled with
 the Heat Conduction Equation", Mathematical Methods in the Applied Sciences, First Online: 16 July 2018 at https://doi.org/10.1002/mma.5077,  Volume 41, Number 13, pp. 5254-5273 (15 September 2018). 

L. Paquet, "Radiative heating of a glass plate: the semi-discrete problem", Afr. Mat.,Volume 29, Issue 1-2, pp.295-330 (2018).

B. Ahounou, L. Paquet, "Existence of a variational solution for the stationary Boussinesq equations with thermocapillary effect and nonhomogeneous boundary conditions", Afr. Mat., Volume 27, Issue 5-6, pp.909-921 (2016).

L. Paquet, "Control of the radiative heating of a glass plate", Afr. Mat., Volume 27, Issue 5-6, pp.673-699 (2016).

L. Paquet, R. El Cheikh, D. Lochegnies, N. Siedow, "Radiative Heating of a Glass Plate", Mathematics In Action, Vol.5,  pp.1-30 (2012).

L. Boulaajine, M. Farhloul, L. Paquet, "A priori error estimation for the dual mixed finite element method of the elastodynamic problem in a poloygonal domain, II", Journal of Computational and Applied Mathematics, Volume 235, pp.1288-1310 (2011). 

L. Paquet, R. Korikache, "Mixed finite element method for the heat diffusion equation in a random medium", Journal of Probability and Stochastic Processes, Volume 82, Issue 6, pp.553-587 (2010).

L. Boulaajine, M. Farhloul, L. Paquet, "A priori error estimation for the dual mixed finite element method of the elastodynamic problem in a poloygonal domain",  Journal of Computational and Applied Mathematics, Volume 231,pp.447-472 (2009).

M. Farhloul, S.Nicaise, L. Paquet, A priori and a posteriori error estimations for the dual mixed finite element method of the Navier-Stokes problem, Numerical Methods for Partial Differential Equations 25:843-869, (2009).

M. Farhloul, S.Nicaise, L. Paquet, Rafilipojaona, Dual mixed finite element methods for the elasticity problem with Lagrange multipliers, Journal of Computational and Applied Mathematics, 221, pp. 224-260 (2008).

M. Farhloul, R. Korikache and L. Paquet, The Dual Mixed Finite Element Method for the Heat Diffusion Equation in a Polygonal domain, I in: Functional Analysis and Evolution Equations The Günter Lumer Volume, H. Amann; W. Arendt; M. Hieber; F. Neubrander; S. Nicaise and J. von Below (Eds), Birkhäuser Verlag, (2008), 239-256.

M. Farhloul, S.Nicaise, L. Paquet, A refined mixed finite element method for the stationary Navier-Stokes equations with mixed boundary conditions.IMA J. Numer. Anal.28 (2008), no. 1, 25--45. 

H. El Sossa and L. Paquet, Refined Mixed Finite Element Method for the Stokes Problem, Canadian Applied Mathematics Quarterly, Volume 15, Number 4, Winter 2007, 375-418.

E. Creusé, M. Farhloul, L. Paquet, A posteriori error estimation for the dual mixed finite element method for the p-Laplacian in a polygonal domain, Comput. Methods Appl. Mech. Engrg. 196 (2007), 2570-2582.

S. Nicaise, L. Paquet, Rafilipojaona, A refined mixed finite element method for the stationary Navier-Stokes equations with mixed boundary conditions using Lagrange multipliers, Com. Meth. Applied Math.,7, 2007, 83-100.

M. Farhloul, S. Nicaise, L. Paquet, A posteriori error estimation for the dual mixed finite element method of the Stokes problem, Numerical Functional Analysis and Optimization, 27(7-8): 831-846, 2006.

L. Boulaajine, M. Farhloul, L. Paquet, A Posteriori Error Estimation for the Dual Mixed Finite Element Method of the Elasticity Problem in a Polygonal Domain, Numer. Methods Partial Differential Eq., 21, (2005), 938-960.

M. Farhloul, S. Nicaise, L. Paquet, A posteriori error estimation for the dual mixed finite element method of the Stokes problem.C.R. Math. Acad. Sci. Paris 339 (2004), no. 7, 513-518. 

M. Jaoua, S. Nicaise, L. Paquet, Identification of cracks with non linear impedances. M2AN Math. Model. Numer. Anal. 37 (2003), 241-257. 

M. Farhloul, L. Paquet, Refined mixed finite element method for the elasticity problem in a polygonal domain.Numer. Methods PDE 18, 323-339 (2002). 

H. El Sossa, L. Paquet, Refined mixed finite element method for the Poisson problem in a polygonal domain with a reentrant corner. Adv. Math. Sci. Appl. 12(2002), no. 2, 607-643.

M. Bourlard, A. Maghnouji, S. Nicaise, L. Paquet, Asymptotic expansion of the solution of a mixed Dirichlet-Ventcel problem with a small parameter. Asymptot. Anal. 28 (2001), no. 3-4, 241-278. 

M. Farhloul, S. Nicaise, L. Paquet, Some mixed finite element methods on anisotropic meshes.M2AN Math. Model. Numer. Anal. 35 (2001), no. 5, 907-920. 

M. Farhloul, S. Nicaise, L. Paquet, Refined mixed finite element method for the Boussinesq equations in polygonal domains.C.R. Math. Acad. Sci. Paris Sér. I Math. 331 (2000), no. 2, 143-148. 

J. M.-S. Lubuma, S. Nicaise, L. Paquet, Integral equations for elliptic problems with edge singularities and applications to the Fourier-boundary element method.Numer. Funct. Anal. Optim. 21 (2000), no. 5-6, 743-779. 

M. Farhloul, S. Nicaise and L. Paquet, A Mixed Finite Element Method of Boussinesq Equations: Some Numerical Results. CFD 99 : proceedings : 7th Annual Conference of the CFD Society of Canada, Halifax, six pages, May 30 to June 1, (1999).

L. Paquet, Regularity of the solutions of the steady-state Boussinesq equations with thermocapillarity effects on the surface of the liquid.Math. Methods Appl. Sci. 22 (1999) no. 12, 1043-1060. 

L. Paquet, The Boussinesq equations in the presence of thermocapillarity at some part of the boundary.Partial differential equations (Han-sur-Lesse, 1993), 266-278, Math. Res., 82,Akademie-Verlag, Berlin, 1994. 

L. Paquet, Precise evaluation of a polynomial at a point given in staggered correction format. Proceedings of the Fifth International Congress on Computational and Applied Mathematics (Leuven, 1992). J. Comput. Appl. Math. 50 (1994), no. 1-3, 433-454. 

L. Paquet, Skeel's condition number for operators in $C\sp 0(\Omega)$ and application to the regularized cogenerator equation of a sub-Markovian resolvent family.Evolution equations, control theory, and biomathematics (Han sur Lesse, 1991), 451-466, Lecture Notes in Pure and Appl. Math., 155, Dekker, New York, 1994. 

L. Paquet, Solutions du problème de Dirichlet sous forme d'un potentiel de simple couche.(French) [Solutions of the Dirichlet problem by means of a single-layer potential] C.R. Acad. Sci. Paris Sér. I Math. 312 (1991), no. 6, 465-470. 

M. Bourlard, S. Nicaise, L. Paquet,An adapted Galerkin method for the resolution of Dirichlet and Neumann problems in a polygonal domain.Math. Methods Appl. Sci. 12 (1990), no. 3, 251--265. 

M. Bourlard, S. Nicaise, L. Paquet,Deux méthodes d'éléments finis frontières raffinés pour la résolution du problème de Neumann dans un polygone.(French) [Two adapted boundary element methods for the solution of the Neumann problem in a polygonal domain] C.R. Acad. Sci. Paris Sér. I Math. 305 (1987), no. 7, 311-314. 

M. Bourlard, S. Nicaise, L. Paquet, Résolution du problème de Dirichlet dans un polygone par éléments finis frontières.(French) [Resolution of the Dirichlet problem in a polygonal domain by the boundary element method] C.R. Acad. Sci. Paris Sér. I Math. 303 (1986), no. 17, 909-912. 

L. Paquet, Opérateurs elliptiques sur les variétés non compactes.(French) [Elliptic operators on noncompact manifolds] J. Funct. Anal.50 (1983), no. 3, 267-284. 

L. Paquet, Problèmes mixtes pour le système de Maxwell.(French) [Mixed problems for the Maxwell system] Ann. Fac. Sci. Toulouse Math., 54(1982), no. 2, 103-141. 

L. Paquet, Formule de Duhamel et problème de la chaleur.(French) [Duhamel's formula and the heat problem] Seminar on Potential Theory, Paris, No. 6, pp. 282-307, Lecture Notes in Math., 906,Springer-Verlag, Berlin-New York, 1982. 

L. Paquet, Méthode de séparation des variables et calcul du spectre d'opérateurs sur les formes différentielles. (French) Bull. Sci. Math., (2), 105(1981), no. 1, 85-112. 

L. Paquet, Semi-groupes généralisés et équations d'évolution. (French) Séminaire de Théorie du Potentiel, No. 4 (Paris, 1977/1978), pp. 243-263, LectureNotes in Math., 713, Springer, Berlin, 1979. 

L. Paquet, Méthode de séparation des variables et calcul de spectre d'opérateurs sur les formes différentielles.(French) C.R. Acad. Sci. Paris Sér. A-B, 289 (1979), no. 2, A107-A110. 

L. Paquet, Semi-groupes holomorphes en norme du sup. (French) Séminaire de Théorie du Potentiel, No. 4 (Paris, 1977/1978), pp. 194--242, Lecture Notes in Math., 713,Springer-Verlag, Berlin, 1979. 

G. Lumer, L. Paquet, Semi-groupes holomorphes, produit tensoriel de semi-groupes et équations d'évolution. (French) Séminaire de Théorie du Potentiel, No. 4 (Paris,1977/1978), pp. 156--177, Lecture Notes in Math., 713,Springer-Verlag, Berlin, 1979. 

L. Paquet, Problèmes mixtes pour le système de Maxwell.(French) C.R. Acad. Sci. Paris Sér. A-B, 289 (1979), no. 3, A191-A194. 

L. Paquet, Problème de Cauchy avec valeurs au bord continues dépendant du temps et comportement asymptotique des solutions.(French) C.R. Acad. Sci. Paris Sér. A-B, 286 (1978), no. 19, A819-A822. 

L. Paquet, Opérateurs locaux dépendant du temps et problème de Cauchy.(French) C.R. Acad. Sci. Paris Sér. A-B 286 (1978), no. 14, A613--A616. 

L. Paquet, Équations d'évolution pour opérateurs locaux et équations aux dérivées partielles.(French) C.R. Acad. Sci. Paris Sér. A-B, 286 (1978), no. 4, A215-A218. 

L. Paquet, Semi-groupes holomorphes en norme uniforme.(French) C.R. Acad. Sci. Paris Sér. A-B,286 (1978), no. 3, A161--A164. 

G. Lumer, L. Paquet, Semi-groupes holomorphes et équations d'évolution.C. R. Acad. Sci. Paris Sér. A-B, t. 284 (1977), no. 4, A237--A240. 
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