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.

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