

Education:
20022005
Doctor of Philosophy in Mathematical
Sciences (May 2005), Carnegie Mellon University, Pittsburgh, USA.
20002002 Master
of Science in Mathematical Sciences,
Carnegie Mellon University.
19961997 Master
of Science in Applied Mathematics, University of Craiova, Romania and Complutense University,
Madrid, Spain.
Dissertation written under
the supervision of Professor C. P. Niculescu and
Professor E. Zuazua.
19911996 Bachelor of Science in Mathematics,
University of Craiova, Romania.
Research interests:
In general: Partial
Differential Equations, Methods in the Calculus
of Variations, Fluid Dynamics.
In particular: Pressureless
Gas Dynamics, MongeKantorovich Optimal Mass
Transportation Theory and Applications to PDE's and Calculus
of Variations, Fourthorder degenerate parabolic
PDE's for thin films, SemiGeostrophic Theory for Atmospheric Flow.
Thesis
title: ``Optimal Mass
Transportation Methods for Gradient Flows in the Weak Topology"
Thesis advisor: Professor David Kinderlehrer.
Research Articles
On
differentiability in the Wasserstein space and wellposedness
for HamiltonJacobi equations (with W. Gangbo), submitted 2017.
Absolutely continuous curves of
probabilities on the line; Eulerian and Lagrangian
descriptions, submitted 2016.
The
SemiGeostrophic system; weakstrong uniqueness under uniform convexity (with M. Feldman), to appear in Calculus of Variations and Partial
Differential Equations (2017).
Chemical
reactiondiffusion networks: convergence of the method of lines (with F. Mohamed & C. Pantea), to
appear in Journal of Mathematical Chemistry (2017), DOI 10.1007/s109100170779z.
Relaxed Lagrangian
solutions for the SemiGeostrophic Shallow Water system in physical space with
general initial data (with M. Feldman), Sankt Petersburg Mathematical J., Vol. 27 (2016)
547568.
Thin
viscous films; thinning driven by surface tension energy dissipation (with F.
Mohamed), J.
of Mathematical Analysis and Applications, Vol. 431, Issue 1 (2015), 111125.
On the
Lagrangian description of absolutely continuous curves in the Wasserstein space
on the line; wellposedness for the Continuity Equation (with M. Amsaad),
Indiana University Mathematics J., Vol. 64 (2015),
18351877.
On the
SemiGeostrophic system in physical space with general initial data (with M.
Feldman), Archive for Rational Mechanics and Analysis, Vol. 218, Issue 1, (2015), 527551.
Onedimensional
pressureless gas systems with/without viscosity (with T. Nguyen), Communications in Partial Differential
Equations, Vol. 40, Issue
9, (2015), 16191665.
Weak
KAM theory on the Wasserstein torus with multidimensional underlying space
(with W. Gangbo), Communications on Pure and
Applied Mathematics, Vol. 67, Issue 3 (2014), 408–463.
On Lagrangian
solutions for the semigeostrophic system with singular initial data (with M.
Feldman), SIAM J. on Mathematical Analysis, Vol. 45, No. 3 (2013), 16161640.
Homogenization
for a class of integral functional in spaces of probabilities measures (with W. Gangbo), Advances in
Mathematics, vol. 230, No. 3 (2012), 11241173.
On a nonlinear, nonlocal parabolic problem with conservation of mass,
mean and variance (with M. Wunsch), Communications in Partial Differential Equations,
Vol. 36, No. 8 (2011), 14261454.
On the velocities of flows consisting of cyclically monotone maps , Indiana
University Mathematics J., Vol. 59, No. 3 (2010), 929956.
A Weak KAM theorem; from
finite to infinite dimension (with W. Gangbo),
Optimal Transportation, Geometry and Functional Inequalities, CRM Series, L. Ambrosio edt., 2010.
Lagrangian Dynamics on an infinite
dimensional torus; a Weak KAM theorem (with W. Gangbo),
Advances in Mathematics, Vol. 224, No.
1 (2010), 260292.
HamiltonJacobi
equations in the Wasserstein space (with W. Gangbo
& T. Nguyen), Methods and Applications of
Analysis (in honour of N. Trudinger),Vol. 15, No.2 (2008), 155184.
Pressureless Euler/EulerPoisson systems
via adhesion dynamics and scalar conservation laws, (with T.
Nguyen), SIAM J. on Mathematical Analysis , Vol. 40, No. 2 (2008),
754775.
Lubrication approximation for
thin viscous films: asymptotic behavior of nonnegative solutions, Communications in Partial
Differential Equations, Vol. 32, No. 7 (2007), 11471172.
EulerPoisson systems as
actionminimizing paths in the Wasserstein space (with W. Gangbo & T. Nguyen), Archive for Rational Mechanics and Analysis, Vol. 192, No.
3 (2009),419452.
On the JKO variational scheme and constrained optimization in the
Wasserstein metric, Calculus of Variations and
Partial Differential Equations, Vol. 32, No. 2 (2008), 155—173
Wasserstein kernels for
onedimensional diffusion problems, Nonlinear Analysis, Vol. 67, No.
9 (2007), 25532572.
Transport via mass
transportation (with D. Kinderlehrer), Discrete and Continuous
Dynamical Systems B, Vol. 6, No. 2 (2006), 311338.
Variational principle for general
diffusion problems (with L. Petrelli), Applied Mathematics and
Optimization, Vol. 50, No. 3 (2004), 229257.
Onephase Stefan problems; a
mass transfer approach, Advances in Mathematical
Sciences and Applications, Vol. 14, No. 1 (2004), 151185.
Work in progress:
Relaxed Lagrangian solutions for the SemiGeostrophicShallowWater
system (with M. Feldman)
Asymptotic decay for dissipative solutions
for thin viscous films (with F. Mohamed)
Heteroclinic orbits for the nonlinear Vlasov system with
periodic potential