Direct problem and inverse problem for the supersonic plane flow past a curved wedge |
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Authors: | Libin Wang |
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Institution: | School of Mathematical Sciences, Fudan University, Shanghai Key Laboratory for Contemporary Applied Mathematics, Laboratory of Mathematics for Nonlinear Science, , Shanghai 200433, China |
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Abstract: | 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. |
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Keywords: | quasilinear hyperbolic system supersonic plane flow shock free boundary problem inverse problem |
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