Quantitative unique continuation for the elasticity system with application to the kinematic inverse rupture problem. Issue 2 (1st February 2023)

• Record Type: Journal Article
• Authors: de Hoop, Maarten V.; Lassas, Matti; Lu, Jinpeng; Oksanen, Lauri
• Is Part Of: Communications in partial differential equations. Volume 48:Issue 2(2023)
• Page Start: 286
• Page End: 314
• Publication Date: 2023-02-01
• Subjects: 35L10 -- 35Q86 -- 35R30; Elasticity -- hyperbolic equations -- kinematic inverse rupture problem -- quantitative unique continuation; Differential equations, Partial -- Periodicals; 515.353
• DOI: 10.1080/03605302.2023.2175215
• Languages: English
• ISSNs: 0360-5302

Abstract

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.