Mathematical Sciences: Research on Nonlinear Partial Differential Equations with Applications to Singular Perturbations, Optimal Control and Differential Games

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This is a project for research on nonlinear partial differential equations with applications to singular perturbations, optimal control theory and differential games, mechanics, nonlinear waves, etc. The general topics of this research include: a) Singular perturbations of reaction-diffusion type; b) First- and second-order PDE's of Hamilton-Jacobi-Bellman-Isaacs type; c) Porous medium equations; d) Nonlinear waves. These topics are unified by the common methodology of partial differential equations. This research is part of applied mathematical analysis.