### Abstract

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.

Original language | English |
---|---|

Pages (from-to) | 1453-1466 |

Number of pages | 14 |

Journal | Mathematical Methods in the Applied Sciences |

Volume | 30 |

Issue number | 12 |

DOIs | |

Publication status | Published - 2007 Aug 1 |

### Fingerprint

### Keywords

- Boundary layer theory
- Initial value problem
- Nonlinear boundary value problems
- Phase plane analysis
- Similarity solution
- Third-order differential equation

### ASJC Scopus subject areas

- Mathematics(all)
- Engineering(all)

### Cite this

*Mathematical Methods in the Applied Sciences*,

*30*(12), 1453-1466. https://doi.org/10.1002/mma.852

**A note on similarity solutions for boundary layer flows with prescribed heat flux.** / Tsai, Je-Chiang; Wang, Ching An.

Research output: Contribution to journal › Article

*Mathematical Methods in the Applied Sciences*, vol. 30, no. 12, pp. 1453-1466. https://doi.org/10.1002/mma.852

}

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 - 2007/8/1

Y1 - 2007/8/1

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

UR - http://www.scopus.com/inward/record.url?scp=34547146931&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34547146931&partnerID=8YFLogxK

U2 - 10.1002/mma.852

DO - 10.1002/mma.852

M3 - Article

VL - 30

SP - 1453

EP - 1466

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

SN - 0170-4214

IS - 12

ER -