Doctor of Philosophy in Mathematical
Sciences (May 2005), Carnegie Mellon University, Pittsburgh, USA.
2000-2002 Master of Science in Mathematical Sciences, Carnegie Mellon University.
1996-1997 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.
1991-1996 Bachelor of Science in Mathematics, University of Craiova, Romania.
In general: Partial
Differential Equations, Methods in the Calculus
of Variations, Fluid Dynamics.
In particular: Pressureless Gas Dynamics, Monge-Kantorovich Optimal Mass Transportation Theory and Applications to PDE's and Calculus of Variations, Fourth-order degenerate parabolic
PDE's for thin films, Semi-Geostrophic Theory for Atmospheric Flow.
title: ``Optimal Mass
Transportation Methods for Gradient Flows in the Weak Topology"
Thesis advisor: Professor David Kinderlehrer.
On differentiability in the Wasserstein space and well-posedness for Hamilton-Jacobi equations (with W. Gangbo), submitted 2017.
The Semi-Geostrophic system; weak-strong uniqueness under uniform convexity (with M. Feldman), to appear in Calculus of Variations and Partial Differential Equations (2017).
Chemical reaction-diffusion networks: convergence of the method of lines (with F. Mohamed & C. Pantea), to appear in Journal of Mathematical Chemistry (2017), DOI 10.1007/s10910-017-0779-z.
Relaxed Lagrangian solutions for the Semi-Geostrophic Shallow Water system in physical space with general initial data (with M. Feldman), Sankt Petersburg Mathematical J., Vol. 27 (2016) 547-568.
Thin viscous films; thinning driven by surface tension energy dissipation (with F. Mohamed), J. of Mathematical Analysis and Applications, Vol. 431, Issue 1 (2015), 111-125.
On the Lagrangian description of absolutely continuous curves in the Wasserstein space on the line; well-posedness for the Continuity Equation (with M. Amsaad), Indiana University Mathematics J., Vol. 64 (2015), 1835-1877.
On the Semi-Geostrophic system in physical space with general initial data (with M. Feldman), Archive for Rational Mechanics and Analysis, Vol. 218, Issue 1, (2015), 527-551.
One-dimensional pressureless gas systems with/without viscosity (with T. Nguyen), Communications in Partial Differential Equations, Vol. 40, Issue 9, (2015), 1619-1665.
Weak KAM theory on the Wasserstein torus with multi-dimensional underlying space (with W. Gangbo), Communications on Pure and Applied Mathematics, Vol. 67, Issue 3 (2014), 408–463.
On Lagrangian solutions for the semi-geostrophic system with singular initial data (with M. Feldman), SIAM J. on Mathematical Analysis, Vol. 45, No. 3 (2013), 1616--1640.
Homogenization for a class of integral functional in spaces of probabilities measures (with W. Gangbo), Advances in Mathematics, vol. 230, No. 3 (2012), 1124--1173.
On a nonlinear, non-local parabolic problem with conservation of mass, mean and variance (with M. Wunsch), Communications in Partial Differential Equations, Vol. 36, No. 8 (2011), 1426--1454.
On the velocities of flows consisting of cyclically monotone maps , Indiana University Mathematics J., Vol. 59, No. 3 (2010), 929--956.
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), 260--292.
Hamilton-Jacobi 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), 155--184.
Pressureless Euler/Euler-Poisson systems via adhesion dynamics and scalar conservation laws, (with T. Nguyen), SIAM J. on Mathematical Analysis , Vol. 40, No. 2 (2008), 754--775.
Lubrication approximation for thin viscous films: asymptotic behavior of nonnegative solutions, Communications in Partial Differential Equations, Vol. 32, No. 7 (2007), 1147--1172.
Euler-Poisson systems as action-minimizing paths in the Wasserstein space (with W. Gangbo & T. Nguyen), Archive for Rational Mechanics and Analysis, Vol. 192, No. 3 (2009),419--452.
Wasserstein kernels for one-dimensional diffusion problems, Nonlinear Analysis, Vol. 67, No. 9 (2007), 2553--2572.
Variational principle for general diffusion problems (with L. Petrelli), Applied Mathematics and Optimization, Vol. 50, No. 3 (2004), 229--257.
One-phase Stefan problems; a mass transfer approach, Advances in Mathematical Sciences and Applications, Vol. 14, No. 1 (2004), 151--185.
Work in progress:
Relaxed Lagrangian solutions for the Semi-Geostrophic-Shallow-Water 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