On existence and multiplicity of similarity solutions to a nonlinear differential equation arising in magnetohydrodynamic Falkner-Skan flow for decelerated flows

Author: 

Naseri, R
Malek, A
Van Gorder, RA

Publication Date: 

30 November 2015

Journal: 

MATHEMATICAL METHODS IN THE APPLIED SCIENCES

Volume: 

38

Last Updated: 

2018-10-09T08:00:57.573+01:00

DOI: 

10.1002/mma.3363

Issue: 

17

page: 

4272-4278

abstract: 

Copyright © 2015 John Wiley & Sons, Ltd. Previously, existence and uniqueness of a class of monotone similarity solutions for a nonlinear differential equation arising in magnetohydrodynamic Falkner-Skan flow were considered in the case of accelerating flows. It was shown that a solution satisfying certain monotonicity properties exists and is unique for the case of accelerated flows and some decelerated flows. In this paper, we show that solutions to the problem can exist for decelerated flows even when the monotonicity conditions do not hold. In particular, these types of solutions have nonmonotone second derivatives and are, hence, a distinct type of solution from those studied previously. By virtue of this result, the present paper demonstrates the existence of an important type of solution for decelerated flows. Importantly, we show that multiple solutions can exist for the case of strongly decelerated flows, and this occurs because of the fact that the solutions do not satisfy the aforementioned monotonicity requirements.

Symplectic id: 

599004

Download URL: 

Submitted to ORA: 

Not Submitted

Publication Type: 

Journal Article