Inéquations variationnelles d'évolution paraboliques du 2ème ordre
Existence, comportement à l'infini et stabilité dans certains problèmes quasilinéaires elliptiques et paraboliques d'ordre 2
Contrôle optimal dans des systèmes gouvernés par des inéquations variationnelles
Optimal control in some variational inequalities
On the controllability of the Laplace equation observed on an interior curve.
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≤...
Optimal control of an ill-posed elliptic semilinear equation with an exponential non linearity
Exact controllability to trajectories for semilinear heat equations with discontinuous diffusion coefficients
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...
Résultats d'existence pour certains problèmes elliptiques quasilinéaires
Nonlinear parabolic equations with natural growth in general domains
We prove an existence result for a class of parabolic problems whose principal part is the -Laplace operator or a more general Leray-Lions type operator, and featuring an additional first order term which grows like . Here the spatial domain can have infinite measure, and the data may be not regular enough to ensure the boundedness of solutions. As a consequence, solutions are obtained in a class of functions with exponential integrability. An existence result of bounded solutions is also given...
Optimal control of an ill-posed elliptic semilinear equation with an exponential non linearity
We study here an optimal control problem for a semilinear elliptic equation with an exponential nonlinearity, such that we cannot expect to have a solution of the state equation for any given control. We then have to speak of pairs (control, state). After having defined a suitable functional class in which we look for solutions, we prove existence of an optimal pair for a large class of cost functions using a non standard compactness argument. Then, we derive a first order optimality system assuming...
Exact controllability to trajectories for semilinear heat equations with discontinuous diffusion coefficients
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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