On Carleman and observability estimates for wave equations on time‐dependent domains

Abstract

We establish new Carleman estimates for the wave equation, which we then apply to derive novel observability inequalities for a general class of linear wave equations. The main features of these inequalities are that (a) they apply to a fully general class of time-dependent domains, with timelike moving boundaries, (b) they apply to linear wave equations in any spatial dimension and with general time-dependent lower-order coefficients, and (c) they allow for significantly smaller time-dependent regions of observations than allowed from existing Carleman estimate methods. As a standard application, we establish exact controllability for general linear waves, again in the setting of time-dependent domains and regions of control.

Locations

• Proceedings of the London Mathematical Society - View - PDF
• arXiv (Cornell University) - View - PDF
• Queen Mary Research Online (Queen Mary University of London) - View - PDF
• DataCite API - View