Uniqueness of solution for ultrahyperbolic equations with lower order terms

TL;DR

This paper establishes various uniqueness results for ultrahyperbolic equations with lower order terms, using Carleman estimates to analyze boundary and interior data, even with domain variations over time.

Contribution

It provides new uniqueness theorems for ultrahyperbolic equations with general lower order terms, including cases with time-dependent domains.

Findings

Uniqueness from boundary data established

Interior data also suffices for uniqueness

Results extend to time-varying domains

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.