Final Report Summary - CONLAWS (Hyperbolic Systems of Conservation Laws: singular limits, properties of solutions and control problems)
The objectives of this research program concerns various theoretic aspects of hyperbolic conservation laws: existence, uniqueness, regularity and fine properties of solutions to hyperbolic systems of conservation laws even in the case of large data. The most important achievements are the description of the fine structure of solutions, the quantitative analysis of the regularizing (compactifying) effect of the semigroup map, the introduction of a new quadratic interaction functional for controlling the compactness estimates of the solutions and the use of convex integration techniques to study turbulence in fluid dynamics. Other important achievements regard the optimality of transport plans, where it is provided a complete answer to the sufficiency of the cyclical monotonicity condition of optimality and to a 30-years old conjecture made by Sudakov. Some of these outstanding results provide a major contribution to the world literature in PDEs.
For dissemination of knowledge, during the development of the project two major international conferences (one of which, the 14th Hyp2012 conference, represents the world's most important event in this area of applied mathematics) and 3 meetings at national level where organized, that have seen the participation of over 700 researchers. The lecture notes of the courses and the proceeding of the conferences are available to the community.
As a conclusion, the project has contributed to further establish the leadership of the Italian school in these field of research developing highly innovative and influential techniques, to exchange ideas and to improve its visibility at the world level, as well as to attract new brilliant young researchers to this very challenging and exciting research field, as for instance Mahir Hadzic (King's College London), Khai T. Nguyen (Penn State University).
For dissemination of knowledge, during the development of the project two major international conferences and 3 meetings at national level where organized, that have seen the participation of over 700 researchers. The lecture notes of the courses and the proceeding of the conferences are available to the community.
As a conclusion, the project has allowed the research group on hyperbolic systems to develop new techniques, to exchange ideas and to improve its visibility at the world level, as well as to attract new brilliant young researchers to this very challenging and exciting research field.
For dissemination of knowledge, during the development of the project two major international conferences (one of which, the 14th Hyp2012 conference, represents the world's most important event in this area of applied mathematics) and 3 meetings at national level where organized, that have seen the participation of over 700 researchers. The lecture notes of the courses and the proceeding of the conferences are available to the community.
As a conclusion, the project has contributed to further establish the leadership of the Italian school in these field of research developing highly innovative and influential techniques, to exchange ideas and to improve its visibility at the world level, as well as to attract new brilliant young researchers to this very challenging and exciting research field, as for instance Mahir Hadzic (King's College London), Khai T. Nguyen (Penn State University).
For dissemination of knowledge, during the development of the project two major international conferences and 3 meetings at national level where organized, that have seen the participation of over 700 researchers. The lecture notes of the courses and the proceeding of the conferences are available to the community.
As a conclusion, the project has allowed the research group on hyperbolic systems to develop new techniques, to exchange ideas and to improve its visibility at the world level, as well as to attract new brilliant young researchers to this very challenging and exciting research field.