Quadratic interaction functional and structure of solutions to hyperbolic conservation laws
|
Thu, 28/02 12:00 |
Stefano Bianchini (SISSA-ISAS) |
OxPDE Lunchtime Seminar  |
Gibson 1st Floor SR |
|
The proof of several properties of solutions of hyperbolic systems of conservation laws in one space dimension (existence, stability, regularity) depends on the existence of a decreasing functional, controlling the nonlinear interactions of waves. In a special case (genuinely nonlinear systems) the interaction functional is quadratic, while in the general case it is cubic. Several attempts to prove the existence of a a quadratic functional also in the most general case have been done. I will present the approach we follow in order to prove this result, an some of its implication we hope to exploit.
Work in collaboration with Stefano Modena. |
|||