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

    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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