Analysis of partial differential equations: nonlinear and asymptotic analysis of parabolic and elliptic systems, study of the well-posedness (existence and uniqueness) and of the stability of solutions.
Mathematical modeling in ferromagnetism: development and study of asymptotic models in ferromagnetism and spintronics, existence and stability of magnetization configurations in ferromagnetic nanowires.
Mathematical study of biological fluids: theoretical study of systems of partial differential equations modeling mucus flow in lungs as well as of an approximate penalized system.
Mathematical modeling in computer science: development and study of fluid models for clusters management.
Transparent boundary conditions: development and study of transparent boundary conditions for dispersive partial differential equations.
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