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