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

    Authors: contact us about adding a copy of your work at [email protected]

    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

    Share

    COinS
     

    Accessibility Statement

    This item was created or digitized prior to April 24, 2027, or is a reproduction of legacy media created before that date. It is preserved in its original, unmodified state specifically for research, reference, or historical recordkeeping. In accordance with the ADA Title II Final Rule, the University Libraries provides accessible versions of archival materials upon request. To request an accommodation for this item, please submit an accessibility request form.