Existence and stability of global solutions of shock diffraction by wedges for potential flow. (English) Zbl 1284.35282
Chen, Gui-Qiang G. (ed.) et al., Hyperbolic conservation laws and related analysis with applications. Selected papers based on the presentations at the workshop at the International Centre for Mathematical Sciences (ICMS) Edinburgh, UK, September 19–23, 2011. Berlin: Springer (ISBN 978-3-642-39006-7/hbk; 978-3-642-39007-4/ebook). Springer Proceedings in Mathematics & Statistics 49, 113-142 (2014).
The authors study shock diffraction by a two-dimensional convex cornered wedge. The problem is formulated as an initial-boundary value problem for the potential flow equation. This problem is invariant with respect to self-similar scale. Then this problem is reduced to the boundary value problem for the first-order nonlinear system of mixed elliptic-hyperbolic type and reformulated as a free boundary problem for nonlinear degenerate first order elliptic system in a bounded domain. Existence and regularity of global self-similar solutions is proved.
For the entire collection see [Zbl 1276.35003].
For the entire collection see [Zbl 1276.35003].
Reviewer: Ilya A. Chernov (Petrozavodsk)
MSC:
| 35L67 | Shocks and singularities for hyperbolic equations |
| 35M12 | Boundary value problems for PDEs of mixed type |
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 35J70 | Degenerate elliptic equations |
| 35L65 | Hyperbolic conservation laws |
| 35R35 | Free boundary problems for PDEs |
| 35J46 | First-order elliptic systems |
Keywords:
mixed type; compressible flow; two-dimensional convex cornered wedge; initial-boundary value problemReferences:
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