On the determination of Moving Boundaries for Hyperbolic Equations

TL;DR

This paper investigates the problem of determining and accessing moving boundaries in wave equations within time-dependent domains, providing conditions for boundary reconstruction from partial boundary data.

Contribution

It introduces sufficient conditions for boundary determination and explores the accessibility of moving boundaries via time-like curves in hyperbolic equations.

Findings

Sufficient conditions for boundary determination from partial data

Analysis of boundary accessibility through time-like curves

Theoretical framework for inverse boundary problems in moving domains

Abstract

We consider wave equations in domains with time-dependent boundaries (moving obstacles) contained in a fixed cylinder for all time. We give sufficient conditions for the determination of the moving boundary from the Cauchy data on part of the boundary of the cylinder. We also study the related problem of accessibility of the moving boundary by time-like curves from the boundary of the cylinder.