Electronic Journal of Differential Equations,
Vol. 2001(2001), No. 62, pp. 1-17.

Title:  Monotone solutions of a nonautonomous differential equation
        for a sedimenting sphere
   
Authors: Andrew Belmonte (Penn State Univ., Univ. Park, PA, USA)
Jon Jacobsen (Penn State Univ., Univ. Park, PA, USA)
Anandhan Jayaraman (Penn State Univ., Univ. Park, PA, USA)
         
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.