Title

High-order nonlinear boundary value problems admitting multiple exact solutions with application to the fluid flow over a sheet

Authors

Authors

R. A. Van Gorder

Comments

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Abbreviated Journal Title

Appl. Math. Comput.

Keywords

Nonlinear boundary value problem; Exact solution; Multiple solutions; Non-Newtonian fluid; NAVIER-STOKES EQUATIONS; HYDROMAGNETIC FLOW; STRETCHING SHEET; SHRINKING; SHEET; HEAT-TRANSFER; VISCOUS-FLOW; SURFACE; Mathematics, Applied

Abstract

We frame a hierarchy of nonlinear boundary value problems which are shown to admit exponentially decaying exact solutions. We are able to convert the question of the existence and uniqueness of a particular solution to this nonlinear boundary value problem into a question of whether a certain polynomial has positive real roots. Furthermore, if such a polynomial has at least two distinct positive roots, then the nonlinear boundary value problem will have multiple solutions. In certain special cases, these boundary value problems arise in the self-similar solutions for the flow of certain fluids over stretching or shrinking sheets; examples given include the flow of first and second grade fluids over such surfaces. (C) 2010 Elsevier Inc. All rights reserved.

Journal Title

Applied Mathematics and Computation

Volume

216

Issue/Number

7

Publication Date

1-1-2010

Document Type

Article

Language

English

First Page

2177

Last Page

2182

WOS Identifier

WOS:000277703300031

ISSN

0096-3003

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