USA-Chile Workshop on Nonlinear Analysis,
Electron. J. Diff. Eqns., Conf. 06, 2001, pp. 109-122.

A semilinear control problem involving homogenization

Carlos Conca, Axel Osses, & Jeannine Saint Jean Paulin

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 RN. 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.

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Carlos Conca
Departamento de Ingenieria Matematica
CMM, UMR 2071 CNRS-Uchile
Universidad de Chile
Casilla 170/3 - Correo 3
Santiago, Chile
e-mail: cconca@dim.uchile.cl
Axel Osses
Departamento de Ingenieria Matematica
CMM, UMR 2071 CNRS-Uchile
Universidad de Chile
Casilla 170/3 - Correo 3
Santiago, Chile
e-mail: axosses@dim.uchile.cl
Jeannine Saint Jean Paulin
Departement de Mathematiques
Universite de Metz
Ile du Saulcy, 57045 Metz Cedex 01, France
e-mail: sjpaulin@poncelet.sciences.univ-metz.fr

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