Nonlinear exact controllability and nonlinear stabilization of hyperbolic or hyperbolic-like evolution equations

Abstract

The present manuscript provides a comprehensive and detailed version of the content of the lectures delivered by the author at the Winter School on Nonlinear Analysis, Instituto de Matematica/UFRJ, August 3-7, 2009, Rio de Janeiro, Brazil. They encompassed two distinct yet related topics: (1) nonlinear global exact controllability, in the space of finite energy, for a second-order hyperbolic equation with Neumannboundary control; and(2) sharp uniform decay rates, at the L2(Ω)-level, of the Schrodinger equation with nonlinear boundary dissipation. ∗Research partially supported by the National Science Foundation under grant NSF-DMS01043-5 and by the Army Research Office under grant ARO-DAAD19-02-1-0179. Mathematics Subject Classification. Primary: 35L05, 35L20. Secondary: 93.