Carleman estimate for ultrahyperbolic operators and improved interior control for wave equations

In this article, we present a novel Carleman estimate for ultrahyperbolic operators, in R t m × R x n . Then, we use a special case of this estimate to obtain improved observability results for wave equations with time-dependent lower order terms. The key improvements are: (1) we obtain smaller obse...
Ausführliche Beschreibung

In this article, we present a novel Carleman estimate for ultrahyperbolic operators, in R t m × R x n . Then, we use a special case of this estimate to obtain improved observability results for wave equations with time-dependent lower order terms. The key improvements are: (1) we obtain smaller observation regions when compared with standard Carleman estimate results, and (2) we also address the case when observability is centered around a point inside the domain. Finally, as a corollary of the observability result, we obtain improved interior controllability for wave equations with same features. Ausführliche Beschreibung