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Well-posedness for non-isotropic degenerate parabolic-hyperbolic equations

Gui-Qiang Chen; Benoît Perthame — 2003

Annales de l'I.H.P. Analyse non linéaire

Free boundary problems and transonic shocks for the Euler equations in unbounded domains

Gui-Qiang Chen; Mikhail Feldman — 2004

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We establish the existence and stability of multidimensional transonic shocks (hyperbolic-elliptic shocks), which are not nearly orthogonal to the flow direction, for the Euler equations for steady compressible potential fluids in unbounded domains in $ℝ^{n}, n \geq 3$ . The Euler equations can be written as a second order nonlinear equation of mixed hyperbolic-elliptic type for the velocity potential. The transonic shock problem can be formulated into the following free boundary problem: The free boundary is the...

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