Research interests:

Research partially supported by NSF Grant DMS-0901340.


A brief description of my research (research statement) can be found here

Curriculum Vitae (updated August 2011)

Preprints:


Anomalous diffusion in plasma physic , Submitted. With L. Cesbron and K. Trivisa

Liquid Drops sliding down an inclined plane , Submitted. With I. Kim

On strong local alignment in the kinetic Cucker-Smale model , Submitted. With T. Karper and K.Trivisa

Existence of weak solutions to kinetic flocking models , Submitted. With T. Karper and K.Trivisa

Existence and asymptotics of fronts in non local combustion models , Submitted. With Y. Sire and J.-M. Roquejoffre

Fractional diffusion limit for collisional kinetic equations: a Hilbert expansion approach , Kinetic and Related Models, accepted. With N. Ben Abdallah and M. Puel

Capillary drops on a rough surface , Interfaces and Free Boundaries Journal, accepted. With J. Nolen.

Electrified thin films: Global existence of non-negative solutions , Annales de l'Institut Henri Poincare - Analyse non lineaire, accepted. With C. Imbert.

Traveling waves for a boundary reaction-diffusion equation, Advances in Mathematics, accepted. With L. Caffarelli and Y. Sire.

Some mathematical aspects of capillary surfaces (review).

Anomalous diffusion limit for kinetic equations with degenerate collision frequency, Math. Models Methods Appl. Sci., accepted. With N. Ben Abdallah and M. Puel.

Publications:


[33] Existence of solutions for a higher order non-local equation appearing in crack dynamics, Nonlinearity 24 (2011) 3487-3514. With C. Imbert.

[32] Fractional diffusion limit for collisional kinetic equations , Arch. Ration. Mech. Anal. 199 (2011), 493-525. With C. Mouhot and S. Mischler

[31] Fractional diffusion limit for collisional kinetic equations: A moments method , Indiana Univ. Math. J. 59 (2010), no. 4, 1333-1360

[30] Existence and regularity of extremal solutions for a mean-curvature equation , J. Differential Equations 249 (2010), 37-75. With J. Vovelle

[29] Homogenization of one-phase Stefan-type problems in periodic and random media , Trans. Amer. Math. Soc. 362 (2010), 4161-4190. With I. Kim

[28] Generalized fronts for one-dimensional reaction-diffusion equations , Discret Cont. Dyn. Syst. 26 (2010) no. 1, 303--312. With Y. Sire and J.-M. Roquejoffre

[27] Stability of Generalized Transition Fronts , Comm. Partia Differential Equations 34 (2009), no. 4-6, 521--552. With J. Nolen, J.-M. Roquejoffre and L. Ryzhik

[26] L^p estimates for quantities advected by a compressible flow, J. of Math. Ana. and App., 355 (2009), no. 2, 548--563. With A. Vasseur.

[25] Homogenization of a Hele-Shaw problem in periodic and random media , Arch. Rat. Mech. Ana., 194 (2009), no. 2, 507-530. With I. C. Kim.

[24] A bound from below for the temperature in compressible Navier-Stokes equations , Monatsh. Math., 157 (2009), no. 2, 143--161. With A. Vasseur.

[23] Random Homogenization of an Obstacle Problem , Ann. Inst. H. Poincare, Anal. Non Lineaire, 26 (2009), no. 2 375--395. With L. Caffarelli.

[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