Education:
2002-2005 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.
1991-1996 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, 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, Chemical
Reaction-Diffusion Networks.
Research
Articles
On a global integral equation arising in the
discretization of granular flows, submitted 2022.
Sticky Particles with Sticky Boundary, submitted 2022.
On the Lagrangian description and uniqueness for the one-dimensional Pressureless Euler system (with M. Suder), Indiana University Mathematics Journal, https://www.iumj.indiana.edu/ IUMJ/Preprints/9354.pdf (2022).
On the convexity condition for the
Semi-Geostrophic system, ESAIM: Control, Optimisation and Calculus of
Variations, Vol. 27 (2021), 1-23.
From Euler to the Semi-Geostrophic System; convergence under uniform convexity (with M. Cullen, M. Feldman), submitted (2020).
Convergence to the complex balanced equilibrium for some chemical reaction-diffusion systems with boundary equilibria (with G. Craciun, J. Jin, C. Pantea), Discrete and Continuous Dynamical Systems-B, doi: 10.3934/dcdsb.2020164.
Heteroclinic orbits for the nonlinear Vlasov and the one-dimensional Vlasov-Poisson systems (with I. Binshati), Nonlinear Analysis, Volume 187 (2019), 180-204.
On differentiability in the Wasserstein space and well-posedness for Hamilton-Jacobi equations (with W. Gangbo), Journal de Mathematiques Pures et Appliquees, Volume 125 (2019), 119-174.
On the Eulerian and Lagrangian descriptions of absolutely continuous curves of probabilities on the line, Discrete and Continuous Dynamical Systems-A, Volume 39, Issue 9 (2019), 5105-5124.
Chemical reaction-diffusion networks: convergence of the method of lines (with F. Mohamed & C. Pantea), Journal of Mathematical Chemistry, Volume 56, Issue 1 (2018), 30-68.
The Semi-Geostrophic system; weak-strong uniqueness under uniform convexity (with M. Feldman), Calculus of Variations and Partial Differential Equations, Volume 56, 158 (2017), https://doi.org/10.1007/s00526-017-1254-1.
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.
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 one-dimensional diffusion problems, Nonlinear Analysis, Vol. 67, No. 9 (2007), 2553-2572.
Transport via mass transportation (with D. Kinderlehrer), Discrete and Continuous Dynamical Systems B, Vol. 6, No. 2 (2006), 311-338.
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.