The boundary approximate controllability of the Laplace equation observed on an interior curve is studied in this paper. First we consider the Laplace equation with a bounded potential. The Lp (1 < p < ∞) approximate controllability is established and controls of Lp-minimal norm are built by duality. At this point, a general result which clarifies the relationship between this duality approach and the classical optimal control theory is given. The results are extended to the Lp (1≤...
The results of this paper concern exact controllability to the trajectories for a coupled system of semilinear heat equations. We have transmission conditions on the interface and Dirichlet boundary conditions at the external part of the boundary so that the system can be viewed as a single equation with discontinuous coefficients in the principal part. Exact controllability to the trajectories is proved when we consider distributed controls supported in the part of the domain where the diffusion...
The results of this paper concern exact controllability to the
trajectories for a coupled system of semilinear heat equations. We
have transmission conditions on the interface and Dirichlet boundary
conditions at the external part of the boundary so that the system can be
viewed as a single equation with discontinuous coefficients in the
principal part. Exact controllability to the trajectories is proved when we
consider distributed controls supported in the part of the domain where the
diffusion...
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