Why people in hyperbolic conservation laws are interested in free boundary problems.
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Free Boundary Problems and Related Topics
In hyperbolic equations, wave propagate with finite velocity. When the equation is quasilinear, this velocity depends on the state itself; this nonconstancy 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 multidimensional setting, where stability is encoded in a Lopatinskii condition.
I’ll also show that in specific problems (steady or selfsimilar solutions), one is naturally led to deal with elliptic equations.
This talk is part of the Isaac Newton Institute Seminar Series series.
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