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Generation of analytic semi-groups in L² for a class of second order degenerate elliptic operators

Cannarsa P., Rocchetti D., Vancostenoble J.

Control and Cybernetics

2008

Vol. 37, no 4

831-878

We study the generation of analytic semigroups in the L² topology by second order elliptic operators in divergence form, that may degenerate at the boundary of the space domain. Our results, that hold in two space dimensions, guarantee that the solutions of the corresponding evolution problems support integration by parts. So, this paper provides the basis for deriving Carleman type estimates for degenerate parabolic operators.

Controllability of semilinear wave equations with infinitely iterated logarithms

Cannarsa P., Komornik V., Loreti P.

Control and Cybernetics

1999

Vol. 28, no 3

449-461

In a previous work we improved some earlier results of Imanuvilov, Li and Zhang, and of Zuazua, on the boundary exact controllability of semilinear wave equations by weakening the growth assumptions on the nonlinearity. Answering a question of Zuazua we give a still weaker, essentially optimal condition. Furthermore, we establish an approximate internal controllability result under the same growth assumptions.