On local controllability of nonlinear hyperbolic equation

Nonlinear Schrödinger Equation on Real Hyperbolic Spaces

We consider the Schrödinger equation with no radial assumption on real hyperbolic spaces. We obtain sharp dispersive and Strichartz estimates for a large family of admissible pairs. As a first consequence, we obtain strong wellposedness results for NLS. Specifically, for small intial data, we prove L 2 and H 1 global wellposedness for any subcritical nonlinearity (in contrast with the flat case...

Local Exact Controllability and Stabilizability of the Nonlinear Schrödinger Equation on a Bounded Interval

This paper studies the exact controllability and the stabilization of the cubic Schrödinger equation posed on a bounded interval. Both internal and boundary controls are considered, and the results are given first in a periodic setting, and next with Dirichlet (resp., Neumann) boundary conditions. It is shown that the systems with either an internal control or a boundary control are locally exa...

Null Controllability of a Nonlinear Heat Equation

On the Exact Controllability of a Nonlinear Stochastic Heat Equation

The bounded open subsetG of Rn is assumed to have a smooth boundary and g is continuous from L2(0,T ;L2(G)) into L2(0,T ;L2(G)). The existence of a solution of the linear version of (1.1) is established in Section 3 of the paper. The nonlinear case is considered in Section 4. The main assumptions of the paper and some preliminary results are given in Section 2. Exact controllability of the wave...

Local exact controllability for Berger plate equation

We study the exact controllability of a nonlinear plate equation by the means of a control which acts on an internal region of the plate. The main result asserts that this system is locally exactly controllable if the associated linear Euler-Bernoulli system is exactly controllable. In particular, for rectangular domains we obtain that the Berger system is locally exactly controllable in arbitr...