A note on similarity solutions for boundary layer flows with prescribed heat flux |
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| Authors: | Je‐Chiang Tsai Ching‐An Wang |
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| Affiliation: | 1. Department of Mathematics, National Chung Cheng University, 168, University Road, Min‐Hsiung, Chia‐Yi 621, TaiwanDepartment of Mathematics, National Chung Cheng University, 168, University Road, Min‐Hsiung, Chia‐Yi 621, Taiwan===;2. Department of Mathematics, National Chung Cheng University, 168, University Road, Min‐Hsiung, Chia‐Yi 621, Taiwan |
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| Abstract: | We study the third‐order nonlinear equation: f′′′ + (m + 2)ff′′ ? (2m + 1)f′2 = 0 on (0, ∞), subject to the boundary conditions f(0) = ? γ ∈ ?, f′(∞) = 0 and f′′(0) = ?1. The problem arises in the study of similarity solutions for boundary layer flows with prescribed heat flux. We will address the following two open questions which were proposed by Brighi and Hoernel (Math. Methods Appl. Sci. 2005; 28 : 479–503): The first one is the uniqueness of bounded solutions for and γ>0, and the second one is the structure of solutions for and γ?0. Copyright © 2007 John Wiley & Sons, Ltd. |
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| Keywords: | nonlinear boundary value problems boundary layer theory similarity solution third‐order differential equation initial value problem phase plane analysis |
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