My research interests include:
Control and Inverse Problems of PDEs
Fractional evolution equations
Semigroups theory
Overview:
My research focuses on the analysis of controllability and inverse problems for partial differential equations. In particular, I develop Carleman estimates to obtain stability estimates and observability inequalities. Then, I apply them to problems with parabolic, hyperbolic, or dispersive systems.
Keywords: Inverse problems, controllability, observability, Carleman estimates, stability estimates, impulse control, dynamic boundary conditions, numerical identification in PDEs, ill-posed problems, time-fractional evolution equations, mean field games systems.