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 |
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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 |
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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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