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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