High-order nonlinear boundary value problems admitting multiple exact solutions with application to the fluid flow over a sheet
Abbreviated Journal Title
Appl. Math. Comput.
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
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.
Applied Mathematics and Computation
"High-order nonlinear boundary value problems admitting multiple exact solutions with application to the fluid flow over a sheet" (2010). Faculty Bibliography 2010s. 881.