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- Title
Existence of transonic shocks in a cylindrical nozzle with given exit normal momentums.
- Authors
Chen, Chao; Wang, Zhiyong
- Abstract
In this paper, we study the existence of transonic shocks in a cylindrical nozzle. More precisely, given the compatible outer normal momentum at the exit of a cylindrical nozzle, there exists a transonic shock solution such that the incoming supersonic flow is compressed to some subsonic flow. The shock position is uniquely determined by the exit normal momentum when we fix one point of the shock. This problem can be reduced to solve a nonlinear free boundary value problem for a hyperbolic–elliptic coupled system and the key ingredient is to solve a second‐order quasilinear elliptic equation with a nonlocal term by the method of separation of variables.
- Subjects
NONLINEAR boundary value problems; TRANSONIC flow; SEPARATION of variables; NOZZLES; SUPERSONIC flow; ELLIPTIC equations
- Publication
Mathematical Methods in the Applied Sciences, 2024, Vol 47, Issue 8, p7056
- ISSN
0170-4214
- Publication type
Article
- DOI
10.1002/mma.9957