PhD research topic - Maurizio FALCONE
Research areas
Numerical Analysis, Mathematical modeling
Keywords
Nonlinear partial differential equations, optimal control, computer vision, granular materials
Research topics
My activity is mainly devoted to numerical methods for nonlinear partial differential equation and to their applications to non linear control problems and games, image processing and granular materials. My research has covered the following topics: semi-Lagrangian schemes for Hamilton-Jacobi equations and conservation laws, finite difference schemes for hyperbolic systems, high-order approximation schemes for nonlinear PDEs, optimal control of nonlinear systems governed by ordinary differential equations and by PDEs, feedback synthesis and optimal trajectories, differential games, pursuit evasion games, 3D reconstruction, segmentation, front propagation, sand piles modeling. For the above topics I have developed approximation schemes, analyzed their properties, proved convergence and a-priori error estimates. A more clear picture of my research activity can be found here https://scholar.google.it/citations?user=Su68Mh4AAAAJ&hl=it
Bibliography
[1] M. Falcone, R. Ferretti, Semi-Lagrangian Approximation Schemes for Linear and Hamilton-Jacobi Equations, SIAM, 2014