Electronic Journal of Differential Equations,
Conference 06 (2001), pp. 109-122.

Title:  A semilinear control problem involving homogenization.

Authors: Carlos Conca (Univ. de Chile, Santiago, Chile) 
  Axel Osses (Univ. de Chile, Santiago, Chile)
  Jeannine Saint Jean Paulin (Univ. de Metz, Ile du Saulcy, France)

Abstract: 
  We consider a  control problem involving a semilinear elliptic equation 
  with a uniformly Lipschitz non-linearity and rapidly oscillating 
  coefficients in a bounded domain of $\mathbb{R}^N$. The control is
  distributed on a compact subset interior to the domain. Given an $N-1$
  dimensional hypersurface at the interior of the domain not
  intersecting the control zone, the trace of the solution on the curve
  has to be controlled. We prove that there exists a limit control as
  the homogenization parameter converges to zero, which results as the 
  limit of fixed points for controllability problems.
  We link this limit control with the corresponding homogenized problem.

Published January 8, 2001.
Math Subject Classifications: 35B37, 35B27, 35J60.
Key Words: control; homogenization; semilinear elliptic equation.