Uniqueness of solution for ultrahyperbolic equations with lower order terms

Abstract

In this article, we prove a variety of uniqueness results for ultrahyperbolic equations with general space and time dependent lower order terms. We address the problem of determining uniqueness of solutions from boundary data as well as when the data is prescribed on an interior subset. Furthermore, we also present the case when the domain may change with respect to any one time component and obtain analogous results. Our main tool for this purpose is Carleman estimate. We obtain different uniqueness results depending on the location of the reference point for the Carleman estimate relative to the domain.

19 pages, 6 figures. This article uses a boundary Carleman estimate from arXiv:2006.16199 to derive a novel interior Carleman estimate and consequently the uniqueness results