Quantitative unique continuation for the elasticity system with application to the kinematic inverse rupture problem

TL;DR

This paper establishes explicit stability estimates for unique continuation in hyperbolic systems, specifically applying to elasticity and Maxwell systems, and uses these results to improve understanding of inverse rupture problems.

Contribution

It provides new explicit stability estimates for the elasticity system and applies these to the inverse rupture problem, advancing the analysis of inverse problems in hyperbolic PDEs.

Findings

Explicit stability estimates for hyperbolic systems

Application to the elasticity and Maxwell systems

Enhanced understanding of inverse rupture problems

Abstract

We obtain explicit estimates on the stability of the unique continuation for a linear system of hyperbolic equations. In particular our result applies to the elasticity system and also the Maxwell system. As an application, we study the kinematic inverse rupture problem of determining the jump in displacement and the friction force at the rupture surface, and we obtain new features on the stable unique continuation up to the rupture surface.