Antoine Mellet, Assistant Professor

Teaching:

Fall 2008: Math 462

Research Interests: Partial Differential Equations and Mathematical Physics

-Analysis of free boundary problems, existence and regularity of viscosity solutions, homogenization.

-Transport Phenomena: Mathematical modeling, kinetic equations (Boltzmann), Fluid equations (Compressible Navier-Stokes), asymptotic analysis, Numerical simulations.

Conferences:

• Workshop Non-local operators and applications (BIRS April 28-May 2nd, 2008)
  
  
• Workshop Analysis of nonlinear PDEs and free boundary problems; Applications to homogenization PIMS-UBC July 20-24, 2009.

Preprints:

Fractional diffusion limit for collisional kinetic equations , submitted. With C. Mouhot and S. Mischler

Stability of Generalized Transition Fronts , submitted. With J. Nolen, J.-M. Roquejoffre and L. Ryzhik

Homogenization of one-phase Stefan-type problems in periodic and random media , submitted. With I. C. Kim.

Homogenization of a Hele-Shaw problem in periodic and random media , Arch. Rat. Mech. Ana., to appear. With I. C. Kim.

A bound from below for the temperature in compressible Navier-Stokes equations , Monatsh. Math., to appear. With A. Vasseur.

Random Homogenization of an Obstacle Problem , Annales de l'IHP, Analyse non lineaire, accepted. With L. Caffarelli.

L^p estimates for quantities advected by a compressible flow, submitted. With A. Vasseur.

Publications:

[22] Random Homogenization of Fractional Obstacle Problems , Netw. Heterog. Media 3 (2008), no. 3, 523--554. With L. Caffarelli.

[21] Asymptotic analysis for a Vlasov-Fokker-Planck/Compressible Navier-Stokes system of equations, Comm. Math. Phys. 281 (2008), no. 3, 573--596. With A. Vasseur.

[20] Capillary drops on an inhomogeneous surface. Perspectives in Nonlinear P.D.E.: In honor of Haim Brezis. Contemporary Mathematics 175--201, Contemp. Math., 446, Amer. Math. Soc., Providence, RI, 2007. With L. Caffarelli.

[19] Existence and uniqueness of global strong solutions for one-dimensional compressible Navier-Stokes equations , SIAM Journal on Mathematical Analysis, 39 (2007/08), no. 4, 1344--1365. With A. Vasseur.

[18] Global weak solutions for a Vlasov-Fokker-Planck/Navier-Stokes system of equations, Math. Models Methods Appl. Sci. 17 (2007), no. 7, 1039--1063. With A. Vasseur.

[17] Homogenization of a nonlinear transport equation , Asymptotic Analysis 51 (2007), 157--166. With A. Vasseur.

[16] Capillary drops on an inhomogeneous surface: Contact angle hysteresis and sticking drop, Calc. Var. Partial Differential Equations 29 (2007), no. 2, 141--160. With L. Caffarelli

[15] On the barotropic compressible Navier-Stokes equations , Comm. Partial Differential Equations 32 (2007), no. 1-3, 431-452, . With A. Vasseur.

[14] Flame propagation in one-dimensional stationary ergodic media, Math. Models Methods Appl. Sci. 17 (2007), no. 1, 155--1699. With L. Caffarelli.

[13] Homogenization and flame propagation in periodic excitable media: The asymptotic speed of propagation , Comm. Pure Appl. Math. 59 (2006), 501-525. With L. A. Caffarelli and K.-A. Lee.

[12] Singular limit and Homogenization for flame propagation in periodic excitable media , Arch. Rat. Mech. Ana., 172 (2004), 153-190. With L. A. Caffarelli and K.-A. Lee.

[11] Numerical comparison between two Spherical Harmonics Expansion models and a kinetic equation , Math. Comput. Modelling, 40 (2004) 777-795. With J.-P. Bourgade, L. Mieussens.

[10] Uniqueness and semigroup for the Vlasov equation with elastic-diffusive reflexion boundary conditions, Applied Math. Lett. 17 (2004), no. 7, 827--832. With S. Mischler.

[9] Macroscopic model for coupled surface and volume collisions in semiconductor superlattices, Asymptotic Analysis 33, (2003), 337-361.

[8] Homogenization and diffusion asymptotics of the linear Boltzmann equation , Control, Optimisation and Calculus of Variations, 9 , (2003), 371--398. With T. Goudon.

[7] On fluid limit for the semiconductors Boltzmann equation , Journal Diff. Equations 189 , (2003), 17--45. With T. Goudon

[6] $L^1$ contraction property for a Boltzmann equation with Pauli statistic , C. R. Acad. Sci. Paris, Ser. I 335 , (2002), 337--340. With B. Perthame.

[5] Discrete version of the SHE asymptotic: Multigroup neutron transport equations , Journal Math. Physics, 43 , (2002), 3232--3260. With T. Goudon.

[4] Diffusion approximation in heterogeneous media, Asymptotic Analysis 28, (2001), 331--358. With T. Goudon.

[3] Diffusion limit of a nonlinear kinetic model without the detailed balance principle , Monatshefte f. Mathematik 134, (2002), 305--329.

[2] Diffusion dynamics of an electron gas between two plates, Methods Appl. Anal. 9 , (2002), 127--150. With P. Degond, V. Latocha and S. Mancini

[1] Electron transport in semiconductor superlattices, Quart. Appl. Math. 61 , (2003), no. 1, 161--192. With N. Ben Abdallah, P. Degond and F. Poupaud.

Ph.D. Thesis: .pdf , .ps