Electron. J. Diff. Eqns., Vol. 2001(2001), No. 62, pp. 1-17.

Monotone solutions of a nonautonomous differential equation for a sedimenting sphere

Andrew Belmonte, Jon Jacobsen, & Anandhan Jayaraman

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.

Submitted January 10, 2001. Published September 24, 2001.
Math Subject Classifications: 34C60, 34D05, 76D03.
Key Words: sedimenting sphere, unsteady Stokes flow, nonautonomous ordinary differential equations, monotone solutions.

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Andrew Belmonte
The W. G. Pritchard Laboratories
Department of Mathematics, Penn State University
University Park, PA 16802 USA
e-mail: belmonte@math.psu.edu

Jon Jacobsen
The W. G. Pritchard Laboratories
Department of Mathematics, Penn State University
University Park, PA 16802 USA
e-mail: jacobsen@math.psu.edu

Anandhan Jayaraman
The W. G. Pritchard Laboratories
Department of Mathematics, Penn State University
University Park, PA 16802 USA
e-mail: anand@math.psu.edu

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