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Francois CASTELLA
IRMAR - Université de Rennes 1
Campus de Beaulieu - 35042 Rennes Cedex - France
email : francois.castella@univ-rennes1.fr

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TRAVAUX, PAR ORDRE CHRONOLOGIQUE
(vous trouverez ici une LISTE PAR THEMES)

F. Castella, B. Perthame, Estimations de Strichartz pour les Equations
de transport Cinétique, ( ps, pdf )
C. R. Acad. Sci. Paris, t. 322, Série I, p. 535-540 (1996).
Nota: Cette Note est un travail à part entière, et ne fera pas l'objet d'une publication ultérieure.

F. Castella, L2-solutions to the Schrödinger-Poisson System : Existence, Uniqueness,
Time Behaviour, and Smoothing Effects, ( ps, pdf )
Math. Mod. Meth. Appl. Sci., Vol. 7, N. 8, pp. 1051-1083 (1997),
et
résultat annoncé dans C. R. Acad. Sci., t. 323, sér. I, p. 1243-1248 (1996).

F. Castella, Effets dispersifs dans les équations de Schroedinger et de Vlasov, ( ps, pdf)
Séminaire Equations aux Dérivées Partielles, 1997-1998, Exp. No. XXIV, 14 pp.,
Ecole Polytechnique, Palaiseau (1998).
Nota: Ce texte est une synthèse des articles "L2-solutions to the Schrödinger-Poisson System ...",
"Estimations de Strichartz pour les Equations de transport Cinétique",
"The Vlasov-Poisson-Fokker-Planck System ...",
et "Propagation of space moments in the Vlasov-Poisson Equation ..."

F. Castella, The Vlasov-Poisson-Fokker-Planck System with infinite kinetic energy, ( ps, pdf )
Indiana Univ. Math. J., Vol. 47, N. 3. p. 939-964 (1998).

F. Castella, Propagation of space moments in the Vlasov-Poisson Equation
and further results, ( ps, pdf )
Ann. I.H.P., Anal. NonLinéaire, Vol. 16, N. 4, p. 503-533 (1999).

F. Castella, On the derivation of a Quantum Boltzmann Equation
from the periodic von Neumann equation, ( ps , pdf )
Math. Mod. An. Num. Vol. 33, N. 2, p. 329-350 (1999).

F. Castella, P. Degond, Convergence de l'équation de von Neumann
vers l'équation de Boltzmann Quantique dans un cadre déterministe, ( ps, pdf )
C. R. Acad. Sci., t. 329, sér. I, p. 231-236 (1999).
Nota: Cette Note annonce une forme plus faible du résultat développé dans les deux articles
"From the von Neumann equation to the Quantum Boltzmann equation ..."
et "From the von Neumann equation to the Quantum Boltzmann equation II ..."

F. Castella, L. Erdös, F. Frommlet, P.A. Markowich, Fokker-Planck equations
as Scaling limits of Reversible Quantum Systems, ( ps , pdf )
J. Statist. Phys., Vol. 100, no. 3-4, pp. 543-601 (2000).

F. Castella, Résultats de convergence et de non-convergence de l'équation
de von Neumann périodique vers l'équation de Boltzmann quantique, ( ps , pdf )
Séminaire E.D.P., Ecole Polytechnique, exposé 1999-2000. N. XXI (2000).
Nota: Ce texte est une synthèse des articles "On the derivation of a Quantum Boltzmann Equation ..."
"From the von Neumann equation to the Quantum Boltzmann equation ..."
"Non derivation of the Quantum Boltzmann equation ..."
et "A distribution result for slices of sums of squares".

F. Castella, From the von Neumann equation to the Quantum Boltzmann equation
in a deterministic framework, ( ps , pdf )
J. Stat. Phys., Vol. 104, N. 1/2, pp. 387-447 (2001).

F. Castella, From the von Neumann equation to the Quantum Boltzmann equation II:
identifying the Born series, ( ps , pdf )
J. Stat. Phys., Vol. 106, N. 5/6, pp. 1197-1220 (2002).

F. Castella, A. Plagne, Non derivation of the Quantum Boltzmann equation
from the periodic von Neumann equation, ( ps , pdf )
Indiana Univ. Math. J., Vol. 51, N. 4, pp. 963-1016 (2002).

F. Castella, A. Plagne, A distribution result for slices of sums of squares,
Math. Proc. Cambridge Philos. Soc., Vol. 132, N.1, pp. 1-22 (2002).

J.D. Benamou, F. Castella, Th. Katsaounis, B. Perthame, High frequency limit
in the Helmholtz equation, ( ps , pdf )
Rev. Mat. Iberoamericana, Vol. 18, N. 1, pp. 187-209 (2002),
et
résultat annoncé dans Séminaire E.D.P., Ecole Polytechnique, exposé N. V, 1999-2000.

F. Castella, B. Perthame, O. Runborg, High frequency limit of the Helmholtz equation II:
source on a general smooth manifold, ( ps , pdf )
Comm. P.D.E., Vol. 27, N. 3-4, pp. 607-651 (2002).

F. Castella, P. Chartier, E. Faou, Analysis of a Poisson system
with boundary conditions, ( ps , pdf )
C. R. Acad. Sci., Sér. I, Vol. 336, pp. 703-708 (2003).
Nota: Cette Note est un travail à part entière, et ne fera pas l'objet d'une publication ultérieure.

D. Benedetto, F. Castella, R. Esposito, M. Pulvirenti, Some considerations
on the derivation of the nonlinear quantum Boltzmann equation, ( ps , pdf )
J. Stat. Phys., Vol. 116, N. 1/4, pp.381-410 (2004).

F. Castella, The Helmholtz equation with source term: high-frequency analysis,
and radiation condition at infinity, ( ps , pdf )
Actes du 36ème Congrès d'Analyse Numérique (CANUM, Obernai) (2004).
Nota: Ce texte est une synthèse des articles "High frequency limit in the Helmholtz equation",
"High frequency limit in the Helmholtz equation II ...",
"Non derivation of the Quantum Boltzmann equation ..."
et "The radiation condition at infinity for the high-frequency Helmholtz equation ...".

F. Castella, The radiation condition at infinity for the high-frequency Helmholtz equation
with source term: a wave packet approach, ( ps , pdf )
Actes du Congrès EDP, Forges-les-Eaux (2004).
Nota: Ce texte est une synthèse de l'article
"The radiation condition at infinity for the high-frequency Helmholtz equation ...".

B. Bidégaray-Fesquet, F. Castella, P. Degond, From Bloch model
to the rate equations, ( ps , pdf )
Disc. Cont. Dyn. Sys., Vol. 11, N. 1, pp. 1-26 (2004).

B. Bidégaray-Fesquet, F. Castella, E. Dumas, M. Gisclon, From Bloch model
to the rate equations II: the case of almost degenerate energy levels, ( ps , pdf )
Math. Mod. Meth. Appl. Sci., Vol. 14, pp. 1785-1817 (2004).

E. Cancès, F. Castella, P. Chartier, E. Faou, C. Le Bris, F. Legoll, G. Turinici,
High-order averaging schemes with error bounds for thermodynamical properties
calculations by molecular dynamics simulations, ( ps , pdf )
J. Chem. Phys., vol. 121, N. 21, pp. 10346--10355 (2004).

F. Castella, P. Chartier, E. Faou, et D. Bayart, F. Leplingard, C. Martinelli (ALCATEL),
Raman Laser: Mathematical and Numerical Analysis of a model, ( ps , pdf )
Math. Mod. An. Num., Vol. 38, N. 3, pp. 457-475 (2004).

F. Leplingard, C. Martinelli, S. Borne, L. Lorcy, T. Lopez, D. Bayart (ALCATEL),
et F. Castella, P. Chartier, E. Faou,
Modeling of multi-wavelength Raman fiber lasers using a new and fast algorithm,
IEEE Photonics Technology Letters, Vol. 16, N. 12, pp. 2601-2603 (2004).

F. Castella, The radiation condition at infinity for the high-frequency Helmholtz equation
with source term: a wave packet approach, ( ps , pdf )
J. Funct. Anal., Vol. 223, pp. 204-257 (2005).

E. Cancès, F. Castella, P. Chartier, E. Faou, C. Le Bris, F. Legoll, G. Turinici,
Long-time averaging for integrable Hamiltonian dynamics, ( ps , pdf )
Numer. Math., Vol. 100, pp. 211-232 (2005).

D. Benedetto, F. Castella, R. Esposito, M. Pulvirenti, On The Weak-Coupling limit
for Bosons and Fermions, ( ps , pdf )
Math. Mod. Meth. Appl. Sci., Vol. 15, N. 12, pp. 1811-1843 (2005).

F. Castella, Th. Jecko, Besov estimates in the high-frequency Helmholtz equation,
for a non-trapping and C^2 potential, ( ps , pdf )
J. Diff. Eq., Vol. 228, N.2, pp. 440-485 (2006).

D. Benedetto, F. Castella, R. Esposito, M. Pulvirenti, Some considerations on the derivation
of the nonlinear quantum Boltzmann equation II: the low density regime, ( ps , pdf )
J. Stat. Phys., Vol. 124, N. 2-4, pp. 951-996 (2006).

F. Castella, P. Degond, T. Goudon, Diffusion dynamics of classical systems
driven by an oscillatory force, ( ps , pdf )
J. Stat. Phys., Vol. 124, N. 2-4, pp. 913-950 (2006).

D. Benedetto, F. Castella, R. Esposito, M. Pulvirenti, A short review on the derivation
of the nonlinear quantum Boltzmann equations, ( ps , pdf )
Comm. Math. Sci., Vol. 5, pp. 55-71 (2007).
Nota: Ce texte est une synthèse des articles
" Some considerations on the derivation of the nonlinear quantum Boltzmann equation",
"On The Weak-Coupling limit for Bosons and Fermions",
et "Some considerations on the derivation of the nonlinear quantum Boltzmann equation II ...".

F. Castella, P. Degond, T. Goudon, Large time dynamics of a classical system
subject to a fast varying force, ( ps , pdf )
Comm. Math. Phys., Vol. 276, N. 1, pp. 23-49 (2007).

F. Castella, P. Degond, T. Goudon, Asymptotic problems for laser-matter modeling:
quantum and classical models, ( ps , pdf )
Nonlinearity, Vol. 20, pp. 1677-1720 (2007).

N. Ben Abdallah, F. Castella, F. Méhats, Moyennisation en temps
pour l'équation de Schrödinger avec fort confinement , ( ps , pdf )
Séminaire E.D.P., Ecole Polytechnique, 2006-2007 (2007).
Nota: Ce texte est une synthèse du résultat obtenu dans l'article "Time averaging ..." ci-dessous.

D. Benedetto, F. Castella, R. Esposito, M. Pulvirenti, From the N-body Schrödinger equation
to the quantum Boltzmann equation: a term-by-term convergence result
in the weak coupling regime. ( ps , pdf )
Comm. Math. Phys., Vol. 277, N. 1, pp. 1-44 (2008).

N. Ben Abdallah, F. Castella, F. Méhats, Time averaging for the strongly confined
nonlinear Schrödinger equation, using almost periodicity ( ps , pdf )
J. Diff. Eq., Vol. 245, N. 1, pp. 154-200 (2008).

F. Castella, Th. Jecko, A. Knauf, Semiclassical resolvent estimates for Schrödinger operators
with Coulomb singularities, ( ps , pdf )
Ann. H. Poincaré, Vol. 9, N. 4, pp. 775-815 (2008).

F. Castella, J.-P. Hoffbeck, Y. Lagadeuc, A reduced model for spatially structured predator-prey systems
with fast spatial migrations and slow demographic evolutions, ( ps , pdf )
Asympt. Anal., Vol. 61, N. 3-4, pp.125-175 (2009).

F. Castella, G. Dujardin, B. Sericola,
Moments analysis in Markov reward models, ( ps , pdf )
Methodol. Comput. Appl. Probab. Vol. 11, N. 4, pp. 583-601 (2009).

N. Ben Abdallah, F. Castella, F. Fendt, F. Méhats, The strongly confined Schrödinger-Poisson system
for the transport of electrons in a nanowire, ( ps , pdf )
SIAM Journal on Applied Mathematics, Vol. 69, N. 3-4, pp. 1162-1173 (2009).

F. Castella, P. Chartier, E. Faou
An averaging technique for highly-oscillatory Hamiltonian problems, ( pdf )
SIAM Journal on Numerical Analysis, Vol. 47, pp. 2808-2837 (2009).

F. Castella, G. Dujardin,
Propagation of Gevrey regularity over long times for the fully discrete Lie Trotter splitting scheme
applied to the linear Schrödinger equation, ( pdf )
Math. Mod. An. Num., Vol. 43, N. 4, pp. 651-676 (2009).

F. Castella, P. Chartier, S. Descombes, G. Vilmart,
Splitting methods with complex times for parabolic equations, ( pdf )
B.I.T., Vol. 49, N. 3, pp. 487-508 (2009).

F. Castella,
Solving ordinary differential equations when the coefficients have low regularity:
a kinetic point of view (after R. Di Perna and P. L. Lions),
Long-range interacting systems, Vol. 11-12, pp. 279-317, Oxford Univ. Press, Oxford (2010).
Nota: Ce texte est une synthèse de l'article original de R. Di Perna et P. L. Lions
sur les équations de transport à coefficients peu réguliers.
Il correspond à un cours donné dans le cadre de l'école de Physique des Houches 2008.

N. Ben Abdallah, F. Castella, Y. Cai, F. Méhats,
Second order averaging for the nonlinear Schrödinger equation
with strong anisotropic potential, ( pdf )
Kinetic and Related Models, Vol. 4, N. 4, pp. 831-856 (2011).

E. Anceaume, F. Castella, B. Sericola,
Analysis of a large number of Markov chains competing for transitions, ( pdf )
Int. J. of Systems Science, Vol. 1, pp. 1-9 (2012).

F. Castella, E. Dumas,
High frequency behavior of the Maxwell-Bloch mdel with relaxations:
convergence to the Schrödinger-rate system, ( pdf )
J. Hyp. Diff. Eq., Vol. 9, N. 3, pp. 1-48 (2012).

F. Castella, S. Madec,
Coexistence phenomena and global bifurcation structure in a chemostat-like model
with species-dependent diffusion rates, ( pdf )
J. Math. Bio. (2012).

F. Castella, A. Klak,
Radiation condition at infinity for the high-frequency Helmholtz equation:
optimality of a non-refocusing criterion, ( pdf )
Hokkaido Math. J. (2012).

E. Anceaume, F. Castella, R. Ludinard, B. Sericola,
Markov Chains Competing for Transitions:
Application to Large-Scale Distributed Systems, ( pdf )
Method. Comp. Appl. Probab., Vol. 15, N. 2, pp. 305-332 (2013).

F. Castella, P. Chartier, F. Méhats, A. Murua,
Stroboscopic averaging for the nonlinear Schrödinger equation, ( pdf )
submitted (2013).

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