Francesca Bucci
Research Interests
Francesca Bucci's research interests lie in the following themes of
Analysis and Control of Partial Differential Equations:
-
mathematical analysis of initial/boundary value problems for evolutionary Partial Differential Equations (PDE), particularly for systems of coupled hyperbolic/parabolic PDE such as thermoelastic systems, models for acoustic-structure or fluid-structure interactions: well-posedness, interior/boundary regularity of the corresponding
solutions;
-
optimal control problems with quadratic functionals for evolutionary linear PDE and composite
systems of PDE, with boundary/interface control; differential and algebraic (operator) Riccati
equations;
-
long-time behaviour of solutions to linear and nonlinear PDEs:
-
uniform stability (or stabilizability), decay rates – via energy methods and
frequency domain techniques;
-
existence of global attractors, along with their structure (fractal dimension,
regularity, etc.);
-
the LQ-problem with non-coercive cost functionals.