### 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 |
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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 |

### 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)

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## Cite this

Tsai, J-C., & Wang, C. A. (2007). A note on similarity solutions for boundary layer flows with prescribed heat flux.

*Mathematical Methods in the Applied Sciences*,*30*(12), 1453-1466. https://doi.org/10.1002/mma.852