Monotone Solutions of a Nonautonomous Differential Equation for a Sedimenting Sphere

Date

2001-09-24

Authors

Belmonte, Andrew
Jacobsen, Jon
Jayaraman, Anandhan

Journal Title

Journal ISSN

Volume Title

Publisher

Southwest Texas State University, Department of Mathematics

Abstract

We study a class of integrodifferential equations and related ordinary differential equations for the initial value problem of a rigid sphere falling through an infinite fluid medium. We prove that for creeping Newtonian flow, the motion of the sphere is monotone in its approach to the steady state solution given by the Stokes drag. We discuss this property in terms of a general nonautonomous second order differential equation, focusing on a decaying nonautonomous term motivated by the sedimenting sphere problem.

Description

Keywords

Sedimenting sphere, Unsteady Stokes flow, Nonautonomous ordinary differential equations, Monotone solutions

Citation

Belmonte, A., Jacobsen, J., & Jayaraman, A. (2001). Monotone solutions of a nonautonomous differential equation for a sedimenting sphere. <i>Electronic Journal of Differential Equations, 2001</i>(62), pp. 1-17.

Rights

Attribution 4.0 International

Rights Holder

Rights License