TY - JOUR
T1 - A note on similarity solutions for boundary layer flows with prescribed heat flux
AU - Tsai, Je Chiang
AU - Wang, Ching An
PY - 2007/8
Y1 - 2007/8
N2 - We study the third-order nonlinear equation: f″′ + (m + 2) f f″ - (2m + 1) f′2 = 0 on (0, ∞), subject to the boundary conditions f(0) = -γ ∈ ℝ, f′(∞) = 0 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 m ∈ (-1, -1/2) and γ>0, and the second one is the structure of solutions for m ∈ (-1, -1/2) and γ>0.
AB - We study the third-order nonlinear equation: f″′ + (m + 2) f f″ - (2m + 1) f′2 = 0 on (0, ∞), subject to the boundary conditions f(0) = -γ ∈ ℝ, f′(∞) = 0 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 m ∈ (-1, -1/2) and γ>0, and the second one is the structure of solutions for m ∈ (-1, -1/2) and γ>0.
KW - Boundary layer theory
KW - Initial value problem
KW - Nonlinear boundary value problems
KW - Phase plane analysis
KW - Similarity solution
KW - Third-order differential equation
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U2 - 10.1002/mma.852
DO - 10.1002/mma.852
M3 - Article
AN - SCOPUS:34547146931
SN - 0170-4214
VL - 30
SP - 1453
EP - 1466
JO - Mathematical Methods in the Applied Sciences
JF - Mathematical Methods in the Applied Sciences
IS - 12
ER -