Title

High-Order Nonlinear Boundary Value Problems Admitting Multiple Exact Solutions With Application To The Fluid Flow Over A Sheet

Keywords

Exact solution; Multiple solutions; Non-Newtonian fluid; Nonlinear boundary value problem

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. © 2010 Elsevier Inc. All rights reserved.

Publication Date

6-1-2010

Publication Title

Applied Mathematics and Computation

Volume

216

Issue

7

Number of Pages

2177-2182

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.amc.2010.03.053

Socpus ID

77953132543 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/77953132543

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