A mixed boundary value problem for Chaplygin's hodograph equation |
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| Authors: | Li Liu Meng Xu Hairong Yuan |
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| Affiliation: | 1. Shanghai University of International Business and Economics, Shanghai 201620, China;2. Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing 210094, China;3. Department of Mathematics, Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, East China Normal University, Shanghai 200241, China |
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| Abstract: | In this paper we will prove existence, uniqueness and regularity of a classical solution to a mixed boundary value problem for Chaplygin's hodograph equation, which is degenerate elliptic on a part of the boundary. This problem is derived from the study of detached bow shock ahead of a straight ramp in uniform supersonic flows in the hodograph plane. The proof depends on Perron's method and some techniques from linear elliptic equations. |
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| Keywords: | Existence Uniqueness Degenerate elliptic equation Chaplygin's equation Perron's method |
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