### Why people in hyperbolic conservation laws are interested in free boundary problems.

**Serre, D ***(UMPA, ENS-Lyon, France )*

Tuesday 13 May 2014, 15:00-16:30

Seminar Room 1, Newton Institute

#### Abstract

In hyperbolic equations, wave propagate with finite velocity. When the equation is quasilinear, this velocity depends on the state itself; this non-constancy leads to the formation of shock waves. Shock waves are inherently free boundaries.
I shall present illustrate basic concepts in one space dimension and discuss a little bit the multi-dimensional setting, where stability is encoded in a Lopatinskii condition.
I'll also show that in specific problems (steady or self-similar solutions), one is naturally led to deal with elliptic equations.

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