On Existence And Multiplicity Of Similarity Solutions To A Nonlinear Differential Equation Arising In Magnetohydrodynamic Falkner-Skan Flow For Decelerated Flows
Keywords
existence theorem; Falkner-Skan flow; multiple solutions; nonlinear boundary value problem
Abstract
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.
Publication Date
11-30-2015
Publication Title
Mathematical Methods in the Applied Sciences
Volume
38
Issue
17
Number of Pages
4272-4278
Document Type
Article
Personal Identifier
scopus
DOI Link
https://doi.org/10.1002/mma.3363
Copyright Status
Unknown
Socpus ID
84955264228 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/84955264228
STARS Citation
Naseri, R.; Malek, A.; and Van Gorder, R. A., "On Existence And Multiplicity Of Similarity Solutions To A Nonlinear Differential Equation Arising In Magnetohydrodynamic Falkner-Skan Flow For Decelerated Flows" (2015). Scopus Export 2015-2019. 852.
https://stars.library.ucf.edu/scopus2015/852