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

Socpus ID

84955264228 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84955264228

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