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Geometric construction of hyperbolic systems of conservation laws

ARGOMENTI: Seminari

SEMINARI DI EQUAZIONI DIFFERENZIALI E APPLICAZIONI
Giovedi' 2 luglio alle ore 12 in aula 2AB/45 TA Kristian Jenssen (Penn State University) "Geometric construction of hyperbolic systems of conservation laws".

-Abstract
We consider the following question: given a frame of smooth vector fields in n-dimensional space; when are these fields the eigenvector fields of a Jacobian matrix? If they are then there is a system of conservation laws with these eigen-fields. We formulate this as a typically overdetermined system of PDEs for the eigenvalues-to-be. The resulting equations are then analyzed using appropriate integrability theorems (Frobenius, Darboux and Cartan-Kaehler). The cases of general systems of three equations, or general rich systems of any size can be resolved completely. Several examples, including the case of gas-dynamics, will be presented to illustrate the general results.

Rif. int. M. Bardi, A. Cesaroni, A. Marson

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