On the stability of an inverse problem for waves via the Boundary Control method

TL;DR

This paper explores the stability of a hyperbolic inverse problem using the Boundary Control method, connecting it to the blowup of constants in unique continuation and controllability, highlighting fundamental limitations.

Contribution

It establishes a theoretical link between stability estimates and blowup phenomena in inverse wave problems using the Boundary Control method.

Findings

Identifies the relationship between stability constants and blowup behavior.

Provides insights into the limitations of control and continuation methods.

Highlights the impact on inverse problem solvability.

Abstract

We establish a link between stability estimates for a hyperbolic inverse problem via the Boundary Control method and the blowup of a constant appearing in the contexts of optimal unique continuation and cost of approximate controllability.