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. Fields of science natural sciencesmathematicsapplied mathematicsmathematical physics Keywords Hyperbolic systems conservation laws regularity properties of solutions singular perturbations weak solutions Programme(s) FP7-IDEAS-ERC - Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Topic(s) ERC-SG-PE1 - ERC Starting Grant - Mathematical foundations 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 EU contribution € 362 000,00 Address VIA BONOMEA 265 34136 Trieste Italy See on map Region Nord-Est Friuli-Venezia Giulia Trieste Activity type Higher or Secondary Education Establishments Principal investigator Stefano Bianchini (Prof.) Administrative Contact Gabriele Rizzetto (Mr.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data Beneficiaries (2) Sort alphabetically Sort by EU Contribution Expand all Collapse all SCUOLA INTERNAZIONALE SUPERIORE DI STUDI AVANZATI DI TRIESTE Italy EU contribution € 362 000,00 Address VIA BONOMEA 265 34136 Trieste See on map Region Nord-Est Friuli-Venezia Giulia Trieste Activity type Higher or Secondary Education Establishments Principal investigator Stefano Bianchini (Prof.) Administrative Contact Gabriele Rizzetto (Mr.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data University of Zurich Switzerland EU contribution € 60 000,00 Address RAMISTRASSE 71 8006 ZURICH See on map Activity type Higher or Secondary Education Establishments Administrative Contact Camillo De Lellis (Prof.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data
