### Abstract

Consideration is given to a class of nonlinear third-order differential equations arising in fluid flow over a nonlinearly stretching sheet. Existence of a solution of the nonlinear third-order differential equation over 0<η<∞ is established in this paper, answering the open question of Vajravelu and Cannon (Appl. Math. Comput. 2006; 181:609-618). That is, we prove with estimates independent of R for solutions of the third-order differential equation on [0,R]. The existence of a solution on 0<η<∞ follows from the Ascoli-Arzela Theorem. Furthermore, numerical solutions are obtained and presented through graphs, and the influence of the physical parameter on the flow characteristics is discussed.

Original language | English |
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Pages (from-to) | 601-606 |

Number of pages | 6 |

Journal | Mathematical Methods in the Applied Sciences |

Volume | 33 |

Issue number | 5 |

DOIs | |

Publication status | Published - Mar 30 2010 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Engineering(all)

### Cite this

*Mathematical Methods in the Applied Sciences*,

*33*(5), 601-606. https://doi.org/10.1002/mma.1181

}

*Mathematical Methods in the Applied Sciences*, vol. 33, no. 5, pp. 601-606. https://doi.org/10.1002/mma.1181

**Similarity solutions of the boundary layer equations for a nonlinearly stretching sheet.** / Akyildiz, F. Talay; Siginer, Dennis A.; Vajravelu, K.; Cannon, J. R.; Van Gorder, Robert A.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Similarity solutions of the boundary layer equations for a nonlinearly stretching sheet

AU - Akyildiz, F. Talay

AU - Siginer, Dennis A.

AU - Vajravelu, K.

AU - Cannon, J. R.

AU - Van Gorder, Robert A.

PY - 2010/3/30

Y1 - 2010/3/30

N2 - Consideration is given to a class of nonlinear third-order differential equations arising in fluid flow over a nonlinearly stretching sheet. Existence of a solution of the nonlinear third-order differential equation over 0<η<∞ is established in this paper, answering the open question of Vajravelu and Cannon (Appl. Math. Comput. 2006; 181:609-618). That is, we prove with estimates independent of R for solutions of the third-order differential equation on [0,R]. The existence of a solution on 0<η<∞ follows from the Ascoli-Arzela Theorem. Furthermore, numerical solutions are obtained and presented through graphs, and the influence of the physical parameter on the flow characteristics is discussed.

AB - Consideration is given to a class of nonlinear third-order differential equations arising in fluid flow over a nonlinearly stretching sheet. Existence of a solution of the nonlinear third-order differential equation over 0<η<∞ is established in this paper, answering the open question of Vajravelu and Cannon (Appl. Math. Comput. 2006; 181:609-618). That is, we prove with estimates independent of R for solutions of the third-order differential equation on [0,R]. The existence of a solution on 0<η<∞ follows from the Ascoli-Arzela Theorem. Furthermore, numerical solutions are obtained and presented through graphs, and the influence of the physical parameter on the flow characteristics is discussed.

UR - http://www.scopus.com/inward/record.url?scp=77949716041&partnerID=8YFLogxK

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U2 - 10.1002/mma.1181

DO - 10.1002/mma.1181

M3 - Article

VL - 33

SP - 601

EP - 606

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

SN - 0170-4214

IS - 5

ER -