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Hyperbolic Systems of Conservation Laws: singular limits, properties of solutions and control problems

Objective

The research program concerns various theoretic aspects of hyperbolic conservation laws. In first place we plan to study the existence and uniqueness of solutions to systems of equations of mathematical physics with physic viscosity. This is one of the main open problems within the theory of conservation laws in one space dimension, which cannot be tackled relying on the techniques developed in the case where the viscosity matrix is the identity. Furthermore, this represents a first step toward the analysis of more complex relaxation and kinetic models with a finite number of velocities as for Broadwell equation, or with a continuous distribution of velocities as for Boltzmann equation. A second research topic concerns the study of conservation laws with large data. Even in this case the basic model is provided by fluidodynamic equations. We wish to extend the results of existence, uniqueness and continuous dependence of solutions to the case of large (in BV or in L^infty) data, at least for the simplest systems of mathematical physics such as the isentropic gas dynamics. A third research topic that we wish to pursue concerns the analysis of fine properties of solutions to conservation laws. Many of such properties depend on the existence of one or more entropies of the system. In particular, we have in mind to study the regularity and the concentration of the dissipativity measure for an entropic solution of a system of conservation laws. Finally, we wish to continue the study of hyperbolic equations from the control theory point of view along two directions: (i) the analysis of controllability and asymptotic stabilizability properties; (ii) the study of optimal control problems related to hyperbolic systems.

Field of science

  • /social sciences/law
  • /natural sciences/mathematics/applied mathematics/mathematical physics

Call for proposal

ERC-2009-StG
See other projects for this call

Funding Scheme

ERC-SG - ERC Starting Grant

Host institution

SCUOLA INTERNAZIONALE SUPERIORE DI STUDI AVANZATI DI TRIESTE
Address
Via Bonomea 265
34136 Trieste
Italy
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 362 000
Principal investigator
Stefano Bianchini (Prof.)
Administrative Contact
Gabriele Rizzetto (Mr.)

Beneficiaries (2)

SCUOLA INTERNAZIONALE SUPERIORE DI STUDI AVANZATI DI TRIESTE
Italy
EU contribution
€ 362 000
Address
Via Bonomea 265
34136 Trieste
Activity type
Higher or Secondary Education Establishments
Principal investigator
Stefano Bianchini (Prof.)
Administrative Contact
Gabriele Rizzetto (Mr.)
University of Zurich
Switzerland
EU contribution
€ 60 000
Address
Ramistrasse 71
8006 Zurich
Activity type
Higher or Secondary Education Establishments
Administrative Contact
Camillo De Lellis (Prof.)