ABSTRACTS BOOK Analytic hypo-ellipticity in the presence of lower order terms

S BOOK Analytic hypo-ellipticity in the presence of lower order terms Paolo Albano University of Bologna, Italy It is well known that the hypoellipticity of a partial differential operator heavily depends on the lower order terms, both in the C∞ and in the analytic category. We consider a second order operator with analytic coefficients whose principal symbol vanishes exactly of order two on a symplectic real analytic manifold. We assume that the first (non degenerate) eigenvalue vanishes on a symplectic submanifold of the characteristic manifold. In the C∞ framework this situation would mean a loss of 3/2 derivatives. We prove that this operator is analytic hypo-elliptic. The main tool is the FBI transform. A case in which the C∞ hypo-ellipticity fails is also discussed. Boundary control problems for hyperbolic equations Fabio Ancona University of Bologna, Italy We will discuss some results concerning the boundary controllability and stabilizzability of first-order hyperbolic equations, where the boundary data are regarded as input-controls. It will be first considered the controllability problem for a scalar hyperbolic conservation laws, and next we will address the problem of asymptotic stabilizzability to constant state for system of conservation laws. As a first step in this direction we will discuss the problem of global exact controllability for first order linear hyperbolic systems with constant coefficients. In particular, we shall consider the case where only a partial control of the boundary values is available. On the determination of thin elastic inclusions from boundary measurements Elena Beretta University of Roma La Sapienza, Italy In this talk we want to present some recent results concerning the identification of thin elastic inclusions in an elastic body from traction-displacement relations measured on the boundary of the region Ω occupied by the body. We accomplish this by deriving a rigorous asymptotic formula of the displacement field u2 with respect to the thickness parameter of the inclusion 2 as 2 → 0.