PDE Methods and Challenges in Control and Inverse Problems

Scope of the special session

Many questions in the applied sciences can be formulated as control problems or inverse problems associated with mathematical models described by partial differential equations (PDE).  The discussion of the proper PDE setting – including, e.g., the understanding of the appropriate boundary conditions to be chosen to develop valid models –, and the analysis of the qualitative and quantitative properties enjoyed by the solutions to these PDE, are of intrinsic interest; in addition, they often constitute a prerequisite step for further investigation.

Issues to be discussed in this special session might include well-posedness of forward problems for PDE in proper (natural) function spaces; availability of interior or boundary trace regularity result; stability properties and decay rates of solutions, in the case of dissipative evolutionary equations. The session specifically welcomes novel contributions within classical topics such as controllability, stabilization, optimal control of PDE systems, under the action of proper controls in the interior of the domain, or localized around some portion  of the boundary. Different topics, included by the broad title of the session, are equally welcome.

In contrast to forward problems, inverse problems are typically ill posed. It is thus important to emphasize the crucial role of the very same PDE methods in order to establish sought properties such as stability/uniqueness for inverse problems, as well as controllability (a major focus of attention for the session). In various control and inverse problems the derivation of appropriate Carleman estimates, observability-type inequalities, or other kinds of PDE estimates becomes a major task. This should readily explain the aim of the organizers to bring together specialists from distinct communities.

Hosting a significant number of young researchers, along renowned specialists, one of the major goals of this session is to foster a fruitful exchange between different generations and contexts.

The organizers of this special session are hopeful that this bringing together of the various participants —mainly but not exclusively from the two partner countries Spain and Italy—, each with his or her unique expertise, will spark fruitful discussions and possible future research work in the study of control and inverse problems.

Organisers

  • Francesca Bucci (University of Florence, Italy) - francesca.bucci@unifi.it
  • Enrique Fernández-Cara (University of Sevilla, Spain)
  • Manuel González Burgos (University of Sevilla, Spain)

Abstracts and schedule

Below you can download the schedule and the abstracts of all talks of this special session.

Speakers

  • Karine Beauchard (École Polytechnique, France)

          Control of Schrödinger-Poisson system

  • Francesca Bucci (University of Florence, Italy)

           Frequency domain analysis and decay rates for a fluid-structure dynamics

  • Piermarco Cannarsa (University of Rome - Tor Vergata, Italy)

           Inverse problems for some classes of degenerate parabolic operators

  • Pedro Caro (University of Helsinki, Finland)

           On global uniqueness for an IBVP for the time-harmonic Maxwell equations

  • Carlos Castro (Polytechnic University of Madrid, Spain)

           Numerical approximation of the inverse scattering problem

  • Michel Cristofol (University of Aix-Marseille, France)

           New kind of observations in an inverse parabolic problem

  • Luz de Teresa (National Autonomous University of Mexico, Mexico)

           Minimal time of controllability for some parabolic systems

  • Giuseppe Floridia (University of Roma - Tor Vergata, Italy)

           Bilinear control of nonlinear degenerate parabolic problems

  • Genni Fragnelli (University of Bari, Italy)

           Identification problems in strongly degenerate parabolic systems

  • Elisa Francini (University of Florence, Italy)

          On the determination of finitely many parameters in some elliptic equations and systems from boundary measurements

  • Elsa Maria Marchini (Polytechnic Institute of Milan, Italy)

           Some relaxation results for state constrained inclusions in infinite dimension, with applications to PDE control problems

  • Francisco Periago (Technical University of Cartagena, Spain)

           Robust shape optimization for stochastic elliptic PDEs

  • Dario Prandi (University of Toulon, France)

           Spectral properties and Aharonov-Bohm effect on Grushin-like structures

  • Fabio Priuli (IAC-CNR, Italy)

           On the controllability for Temple class systems with characteristic boundary

  • Diego Araujo de Souza (University of Sevilla, Spain)

           On the uniform control of some alpha-models