Hyperbolic boundary problems, Carleman estimates, and the Kreiss-Sakamoto-Tataru condition

Abstract: A review of the theory of hyperbolic initial-boundary value problems is presented. Since the 1970s there are two competing theories, one for symmetric hyperbolic systems mainly due to Friedrichs and one for strictly hyperbolic systems due to Kreiss and Sakamoto. The relationship of these two theories has been clarified only during the last decade. A central part of both theories is played by a priori estimates. Carleman estimates share some similarities with hyperbolic a priori estimates. Initially establish for functions with compact support and as a tool for proving unique continuation for operators with non-analytic coefficients, they have found applications in Inverse Problems and Control Theory. Boundary data were included in Carleman estimates by Lebeau, Robbiano, and Tataru established a condition similar to the one used by Kreiss and Sakamoto for hyperbolic problems. The case of scalar second-order operators will be discussed.

Mathematics

Audience: researchers in the topic

International Zoom Inverse Problems Seminar, UC Irvine