Stability Estimates for an Inverse Hyperbolic Initial Boundary Value Problem with Unknown Boundaries

TL;DR

This paper establishes logarithmic stability estimates for an inverse problem involving unknown boundary determination in an anisotropic wave equation, based on finite time boundary observations.

Contribution

It provides the first stability estimates of logarithmic type for boundary reconstruction in anisotropic wave equations with unknown boundaries.

Findings

Proves logarithmic stability estimates for the inverse boundary problem.

Demonstrates the feasibility of boundary determination from finite time boundary data.

Extends inverse problem theory to anisotropic wave equations with unknown boundaries.

Abstract

In this paper we prove stability estimates of logarithmic type for an inverse problem consisting in the determination of unknown portions of the boundary of a domain in $\mathbb{R}^n$, from a knowledge, in a finite time observation, of overdetermined boundary data for initial boundary value problem for anisotropic wave equation.