Activités de Recherche / Research Activities
- Thèmes de recherche - Résumé de mes travaux en 2 pages (2008)
Analyse
Théorique et Numérique de l'équation de Boltzmann
Equations
cinétiques posées dans un domaine
Equations
de Boltzmann pour les gaz de particules
Equations
de Coagulation-fragmentation
Dynamiques
de populations structurées
Collisions
inélastiques
- Articles et notes originales dans des revues avec
comités de lecture, Notes originales
[1] S. Mischler, Uniqueness for the
B.G.K.-equation in R^N and rate of convergence for a
semi-discrete scheme, Differential and Integral Equations 9 No 5 (1996), 1119-1138
[2] L. Desvillettes et S. Mischler, About
the splitting algorithm for Boltzmann and B.G.K. equations,
Mathematical Models and Methods in Applid Sciences 6 No. 8 (1996),
1079-1101
[3] S. Mischler, Convergence of
discrete velocities schemes for the Boltzmann equation, Archive
for Rational Mechanics and Analysis 140
(1997), 53-77
[4] S. Mischler, B. Perthame, Boltzmann
equation with infinite energy: Renormalized solutions and
distributional solutions for small initial data and initial data close
to a Maxwellian, SIAM Journal of Mathematical Analysis 28 No 5 (1997), 1015-1027
[5] S. Mischler, B. Wennberg, On the
Spatially Homogeneous Boltzmann equation, Annales de
l'Institut Henri Poincaré - AN 16
No 4 (1999), 467-501
Récompensé
par le
prix Institut Henri Poincaré / Gauthier-Villars
[6] S. Mischler, On the trace problem
for solutions
of the Vlasov equation, Comm. Partial Differential Equations 25 No 7-8 (2000), 1415-1443 (version
préprint en .pdf)
[7] S. Mischler, On the initial
boundary value problem for
the Vlasov-Poisson-Boltzmann
system, Comm. Math. Phys. 210
No 2 (2000), 447-466 (version
preprint en .pdf)
[9] M. Escobedo, S. Mischler, On a
Quantum Boltzmann equation
for a gas of photons, J. Math. Pures Appl. 80 No 5 (2001), 471-515 (version
preprint en .pdf)
[11] Ph. Laurençot, S. Mischler, Global existence for the discrete diffuse
coagulation-fragmentation equations in L^1, Rev. Mat.
Iberoamericana 18 (2002),
221-235 (version
preprint
en .pdf)
[12] Ph. Laurençot, S. Mischler, The continuous
coagulation-fragmentation equations with diffusion, Arch.
Rational Mech. Anal. 162 No 1
(2002), 45-99 (version
preprint en .pdf)
[13] M. Escobedo, S. Mischler, J.J.L. Velazquez, Asymptotic description of Dirac mass
formation in kinetic equations for quantum particles,
J. Differential Equations 202 No
2 (2004) 208-230 (version
preprint en .pdf)
[14] Ph. Laurençot, S. Mischler, From the discrete to the continuous
coagulation-fragmentation equations, Proc. Roy. Soc.
Edinburgh 132A (2002),
1219-1248 (version
preprint en .pdf)
[15] M. Escobedo, S. Mischler, B. Perthame, Gelation in coagulation and fragmentation
models, Comm. Math. Phys. 231
1, (2002), 157-188 (version
preprint en .pdf)
[16] Ph. Laurençot, S. Mischler, The Lifshitz-Slyozov-Wagner asymptotic of
th Becker-Döring equation, J. Statist. Phys. 106 No. 5-6 (2002), 957-991 (version
preprint en .pdf)
[17] M. Escobedo, S. Mischler, M. Del Valle, Maximization entropy problem for Quantum
and Relativistic particles, Bulletin de la SMF 133 (2005) 87-120 (version
preprint en .pdf)
[18] M. Escobedo, S. Mischler, M. Del Valle, Homogeneous Boltzmann equation for Quantum
and Relativistic particles, Electron. J. Diff. Eqns.,
Monograph 04 (2003), 85 pages (http://ejde.math.swt.edu/) (version
preprint en .pdf)
[19] T. Horsin, S. Mischler, A. Vasseur, On the convergence of numerical schemes for
the Boltzmann equation, Annales de l'Institut Henri
Poincaré - AN 20 No 5
(2003), 731-758 (version
preprint en .pdf)
[20] A. Mellet, S. Mischler, Uniqueness
and semigroup for the Vlasov
equation with elastic-diffusive reflexion boundary conditions,
Appl. Math. Lett. 17
No. 7 (2004) 827-832 (version
preprint en .pdf)
[21] S. Mischler, B. Perthame, L. Ryzhik, Stability in a Nonlinear Population
Maturation Model, Mathematical Models and Methods in Applid
Sciences 12 No. 12 (2002),
1-22 (version
preprint en .pdf)
[22] Ph. Laurençot, S. Mischler, Convergence to the equilibrium for the
coagulation-fragmentation equation, Bulletin des Sciences
Mathématiques 127 No. 3
(2003), 179-190 (version
preprint en .pdf)
[23] M. Escobedo, Ph. Laurençot, S. Mischler, B. Perthame,
Gelation and mass conservation in
coagulation-fragmentation models, J. Differential
Equations 195 No 1
(2003) 143-174 (version
preprint en .pdf)
[24] M. Escobedo, Ph. Laurençot, S. Mischler, Fast reaction limit for
coagulation-fragmentation equation, Comm. Partial
Differential Equations 28 No 5
& 6 (2003) (version
preprint en .pdf)
[25] S. Mischler, M. Rodriguez Ricard, Existence
globale pour l'équation de
Smoluchowski continue non homogène et comportement asymptotique
des solutions, C.R. Acad. Sc. Paris série I 336 (2003), 407-412 (version
preprint en .pdf)
[26] M. Escobedo, P. Laurençot, S. Mischler, On a kinetic equation for coalescing
particles, Comm. Math. Phys. 246 No 2 (2004) 237-267 (version
preprint en .pdf)
[30] N. Fournier, S. Mischler, Exponential
trend to equilibrium for
discrete coagulation equations with strong fragmentation and without a
balance condition, Proc. R. Soc. Lond. Ser. A Math. Phys.
Eng. Sci. 460 No. 2049
(2004) 2477-2486 (version
preprint en .pdf)
[31] N. Fournier, S. Mischler, On a
Boltzmann Equation for elastic,
inelastic and coalescing collisions, J. Math. Pures Appl. (9) 84
(2005), no. 9, 1173–1234 (version
preprint en .pdf)
[32] M. Escobedo, S. Mischler, M. Rodriguez Ricard, On self-similarity and stationary problem
for fragmentation and coagulation models, Ann. Inst. H.
Poincaré Anal. Non Linéaire 22 No. 1 (2005) 99-125 (version
preprint en .pdf)
Récompensé
par le
prix Institut Henri Poincaré / Gauthier-Villars
[34] N. Ben Abdallah, M. Escobedo, S. Mischler, Convergence to the equilibrium for the
Pauli equation without detailed balance condition, C. R.
Math. Acad. Sci. Paris 341 (2005), no. 1, 5–10 (version
preprint en .pdf)
[35] P. Laurençot, S. Mischler, Liapunov
functionals for Smoluchowski's
coagulation equation and convergence to self-similarity,
Monatsh. Math. 146 (2005), no. 2, 127–142 (version
preprint en .pdf)
[36] S. Mischler, C. Mouhot, M. Rodriguez Ricard, Cooling process for inelastic Boltzmann
equations for hard spheres, Part I: The Cauchy Problem, J. Stat.
Phys. 124 (2006), no. 2-4, 655–702 (version
preprint en .pdf)
[37] S. Mischler, C. Mouhot, Cooling
process for inelastic Boltzmann
equations for hard spheres, Part II: Existence of self-similar
solutions and proof of Haff's law, J. Stat. Phys. 124 (2006),
no. 2-4, 703–746 (version
preprint en .pdf)
[38]
M. Escobedo, S. Mischler, On
self-similarity for the coagulation
equation, Ann. Inst. H. Poincaré Anal. Non
Linéaire 23 (2006), no. 3, 331–362 (version
preprint en .pdf)
[39] O. Diekmann, P.-E. Jabin, S. Mischler, B. Perthame, The dynamics of adaptation : an
illuminating example and a Hamilton-Jacobi approach, Theoretical
Population Biology 67 (2005) 257-271. (version
preprint en .pdf)
[40] M. Escobedo, S.Mischler, J.J.L.Velazquez, On the fundamental solution of a linearized
Uehling-Uhlenbeck equation, Arch. Rational Mech. Anal. 186
(2007), 309–349 (version
preprint en .pdf)
[41] P. Michel, S. Mischler, B. Perthame, General relative entropy inequality: an
illustration on growth models, J. Math. Pures Appl. (9) 84
(2005), 1235–1260. (version
preprint en .pdf)
[43] M. Escobedo, S. Mischler, J.J.L.Velazquez, Singular Solutions for the Uehling
Uhlenbeck Equation, Proceedings of the Royal Society of
Edinburgh, 138A (2008), 67–107 (version
preprint en .pdf)
[44] L. Desvillettes, P.-E. Jabin, S. Mischler, G. Raoul, On selection dynamics for continuous structured populations, Comm. Math.
Sci., (3) 6, (2008), 729-747 (version
preprint en .pdf)
[45] S. Mischler, C. Mouhot, Stability,
convergence to self-similarity and elastic limit for the Boltzmann
equation for inelastic hard spheres, Comm. Math. Phys., (3) 287,
(2009) HAL:
hal-00124876
[46] S. Mischler, C. Mouhot, Convergence
to the steady state and elastic limit for the Boltzmann equation for
diffusively excited inelastic hard spheres, Discrete and Cont.
Dyn. Syst. Series A (2009), vol. 24, pp 159-185, HAL:
hal-00193200
[47] J.A. Cañizo, S. Mischler, Regularity,
asymptotic behavior and partial uniqueness for Smoluchowski’s
coagulation equation, arXiv:0803.1462v2,
accepté pour publication dans Rev. Mat. Iberoamericana
[48] J.A. Cañizo, S. Mischler, C. Mouhot, Rate of convergence to self-similarity for
the Smoluchowski coagulation equation with constant coeficient,
SIAM Journal on Mathematical Analysis, (2010), vol. 41 (no. 6), pp
2283-2314, HAL:
hal-00337661
[49] A. Mellet, S. Mischler, C. Mouhot, Fractional diffusion limit for collisional
kinetic equations, accepté pour publication dans Arch.
Rational Mech. Anal. HAL:
hal-00321478
[50] S. Mischler, M. Rodriguez Ricard, Turing
instabilities at Hopf bifurcation, Journal of Nonlinear Science
vol. 19 (2009), no. 5, 467–496. Récompensé
par le prix annuel 2009 de l’Académie des Sciences de Cuba
- Prépublications
/ Nouveautés
Après un long processus de révision, un de mes articles
préférés a enfin été publié:
[10] S. Mischler, Kinetic equations
with Maxwell boundary
condition, Annales scientifiques de l’ENS 43, fascicule 5 (2010),
719-760 (dernière
version
preprint en .pdf, version
HAL)
[51]
M. Escobedo, S. Mischler, Self-similarity
for ballistic aggregation equation, J. Stat. Phys. 141 (2010), hal-00429213
[52] S. Mischler, C. Mouhot, Quantitative
uniform in time chaos propagation for Boltzmann collision processes,
hal-00447988
[53] M.P. Gualdani, S. Mischler, C. Mouhot, Factorization for non-symmetric operators
and exponential H-theorem, http://hal.archives-ouvertes.fr/ccsd-0049578
[54] A. Arnold, I.M. Gamba, M.P. Gualdani, S. Mischler, C. Mouhot, C.
Sparber, The Wigner-Fokker-Planck equation: Stationary states
and large time behavior, arXiv:1010.2791v1
[55] J.A. Cañizo, M. J. Caceres, S. Mischler, Rate of convergence to the remarkable state
for fragmentation and growth-fragmentation equations,
accepté pour publication dans J. Math. Pures Appl., http://arxiv.org/abs/1010.5461
[56] S. Mischler, C. Mouhot, B. Wennberg, A new approach to quantitative chaos
propagation for drift, diffusion and jump processes, (version
preprint en .pdf)
[57] J.A. Cañizo, M. J. Caceres, S. Mischler, Rate of convergence to self-similarity for
the fragmentation equation in L^1 spaces, http://arxiv.org/abs/1102.3661
[58] S. Mischler, Le programme de
Kac sur les limites de champ moyen, séminaire
EDP-X, (version
preprint en .pdf)
[59] M. Hauray, S. Mischler, On Kac's
chaos and related problems, (version
preprint en .pdf)
Articles de "Survey", Rapports, Notes
annonçant un
résultat, Actes de
Congrès
[8] M. Escobedo, S. Mischler, Equation
de Boltzmann Quantique pour un gaz
de photons, Note au C.R. Acad. Sc. Paris série I 329 (1999), 593-598 (version
preprint en .pdf)
[27] J. Clairambault, B. Laroche, S. Mischler, B. Perthame, A mathematical model of cell-cycle and its
control, Rapport de recherche INRIA n. 4892 (2003) (version
preprint en .pdf)
[28] N. Fournier, S. Mischler, On a
discrete Boltzmann-Smoluchowski
Equation with bounded rate in the velocity variables,
Commun. Math. Science 2,
Supplemental issue 1 (guest editors François Golse, Thierry
Goudon, Frédéric Lagoutière) (2004) 55--63.
Proceeding de la conférence GRIP (groupe de recherche sur les
interactions de particules) sur les phénomènes de
coagulation et fragmentation (version
preprint en .pdf)
[29] P. Laurençot, S. Mischler, On
coalescence equations and related models,
article de "survey" dans Modeling and computational methods for
kinetic equations, Editors P. Degond, L. Pareschi, G.
Russo, 321--356, Model. Simul. Sci. Eng. Technol.,
Birkhäuser Boston, Boston, MA, 2004 (version
preprint en .pdf)
[33] P. Michel, S. Mischler, B. Perthame, General entropy equations for structured
population models and scattering, C.R. Acad. Sc. Paris
série I 338 (2004),
697-702
[42] M. Escobedo, S. Mischler, Qualitative
properties of some Boltzmann like equations which do not fulfill a
detailed balance condition,
notes of a summer school in
Santander, Spain, july 2004, publié dans Recent trends in
partial
differential equations, 95–123, Contemp. Math., 409, Amer. Math. Soc.,
Providence, RI, 2006 (version
preprint en .pdf)
- Documents de travail, Conférences, Notes
personnelles, Exposés
- Mecanismos de crecimiento: desde el modelaje hasta el
anàlisis
matemàtico, Jornada del 50to egresado del
Doctorado en Matemàtica de la UCV, Caracas, Venezuela (version
.pdf)
- Quantitative and uniform in time chaos convergence for
N-particle system to its single-typical-particle statistical
limit, Paris 6, Barcelona, Lyon 1, X-EDP 2010 (version
.pdf)
- Preserving hypocoercivity when enlarging the space
setting for linear PDE and
applications, Oberwolfach 2010 (version
.pdf)
- Chaos and Statistical solutions, congress: "Boltzmann
equation: mathematics, modeling and simulations In memory of Carlo
Cercignani" - IHP, Paris, February 2011 (version
.pdf)
- Cours de l’Ecole doctorale EDDIMO : Estimation
quantitative et uniforme en temps de la propagation du chaos et
introduction aux limites de champ moyen pour des syst`emes de
particules
mars 2011, (version
provisoire.pdf)
- An inverse solution to Kac's program in mean-field
theory, "Kinetic models of classical and quantum particle systems" A
conference in memory of Naoufel Ben Abdallah, IMT, Toulouse, March
14-18, 2011 (version
.pdf)
- Kac's program in kinetic
theory, Séminaire Analyse Numérique et EDP,
Université Lille 1, 20 Octobre 2011 (version
.pdf)
- Habilitation à Diriger des recherches / Second
Thesis
Ecole Doctorale : Ecole Doctorale de Sciences
Mathématiques de Paris Centre
Titre : Contributions
à
l'étude mathématique de quelques
modèles issus de la physique statistique hors
équilibre (version
.pdf)
Date et lieu de soutenance : 12 décembre 2001
à l'Université de Versailles Saint-Quentin
Jury : Pierre Degond (rapporteur), Laurent
Desvillettes, François Golse, Otared Kavian, Benoît
Perthame, Jean-Pierre Puel, Mario Pulvirenti (rapporteur), Juan J.L.
Velazquez
- Conférences organisées:
Website of "EDP y aplicaciones" session, 8th Int. Conf. OR,
February 2008, La
Habana, Cuba
Website
of the Winter School
and 9th ICOR sessions on PDE and Mathematical Biology
February
2010,
La Habana, Cuba
"PDE and probability"
session 10th ICOR conference, March 2012, La
Habana, Cuba