Carleman Estimates for Elliptic Boundary Value Problems with Applications to the Stabilization of Hyperbolic Systems

Matthias Eller* and Daniel Toundykov

A Carleman estimate for some first-order elliptic systems is established. This estimate is extended to elliptic boundary value problems provided the boundary condition satisfies a Lopatinskii-type requirement. Based on these estimates conservative hyperbolic systems of first order can be stabilized with a logarithmic decay rate by introducing a localized interior dissipation. The support of the dissipative term does not need to satisfy a geometric condition.

Mathematics Subject Classification: 35J56 93D15

Keywords: Carleman estimates for elliptic systems, stabilization, hyperbolic systems of first order

Minisymposion: Harmonic Analysis with Applications to Uniqueness and Inverse Estimates for PDEs