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Direct problem and inverse problem for the supersonic plane flow past a curved wedge
Author(s) -
Wang Libin
Publication year - 2011
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1530
Subject(s) - wedge (geometry) , uniqueness , supersonic speed , transonic , conservative vector field , mathematics , choked flow , shock (circulatory) , inverse , plane (geometry) , flow (mathematics) , inverse problem , mathematical analysis , geometry , mechanics , physics , aerodynamics , compressibility , medicine
In this paper, we consider the isentropic irrotational steady plane flow past a curved wedge. First, for a uniform supersonic oncoming flow, we study the direct problem: For a given curved wedge y = f ( x ), how to globally determine the corresponding shock y = g ( x ) and the solution behind the shock? Then, we solve the corresponding inverse problem: How to globally determine the curved wedge y = f ( x ) under the hypothesis that the position of the shock y = g ( x ) and the uniform supersonic oncoming flow are given? This kind of problems plays an important role in the aviation industry. Under suitable assumptions, we obtain the global existence and uniqueness for both problems. Copyright © 2011 John Wiley & Sons, Ltd.