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 June 2013)


Preprints:


Regularity of local minimizers of the interaction energy via obstacle problems , submitted. With J. Carrillo and M. Delgadino

Self-Similar Solutions for a Fractional Thin Film Equation Governing Hydraulic Fractures. Comm. Math. Phys. Accepted. With C. Imbert.


Publications:

[47] Anomalous energy transport in FPU-beta chain. J. Stat. Phys. 160 (2015). With S. Merino-Aceituno.

[46] Hydrodynamic limit of the kinetic Cucker-Smale flocking model , Math. Models Methods Appl. Sci. 25 (2015) With T. Karper and K.Trivisa

[45] The thin film equation with non zero contact angle: A singular perturbation approach. Comm. Partial Differential Equations 40 (2015).

[44] Liquid Drops sliding down an inclined plane , Trans. Amer. Math. Soc. 366 (2014). With I. Kim

[43] On strong local alignment in the kinetic Cucker-Smale model , Hyperbolic conservation laws and related analysis with applications, Springer Proc. Math. Stat., 49, Springer, Heidelberg, 2014. With T. Karper and K.Trivisa

[42] Existence and asymptotics of fronts in non local combustion models , Commun. Math. Sci. 12 (2014). With Y. Sire and J.-M. Roquejoffre

[41] Existence of weak solutions to kinetic flocking models , SIAM J. Math. Anal. 45 (2013). With T. Karper and K.Trivisa

[40] Some mathematical aspects of capillary surfaces Singularities in mechanics: formation, propagation and microscopic description, 91-124, Panor. Synth¸ses, 38, Soc. Math. France, Paris, 2012.

[39] Anomalous diffusion in plasma physic , Appl. Math. Lett. 25 (2012). With L. Cesbron and K. Trivisa

[38] Capillary drops on a rough surface , Interfaces Free Bound. 14 (2012). With J. Nolen.

[37] Electrified thin films: Global existence of non-negative solutions , Ann. Inst. H. Poincare Anal. Non Lineaire 29 (2012). With C. Imbert.

[36] Traveling waves for a boundary reaction-diffusion equation, Adv. Math. 230 (2012). With L. Caffarelli and Y. Sire.

[35] Fractional diffusion limit for collisional kinetic equations: a Hilbert expansion approach , Kinet. Relat. Models 4 (2011). With N. Ben Abdallah and M. Puel

[34] Anomalous diffusion limit for kinetic equations with degenerate collision frequency, Math. Models Methods Appl. Sci. 21 (2011). With N. Ben Abdallah and M. Puel.

[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