Uniqueness in Inverse Problems for Elastic Media with Residual Stress

DOI10.1081/PDE-120025485zbMath1060.35165OpenAlexW2077380188MaRDI QIDQ4446118

Lizabeth V. Rachele

Publication date: 25 January 2004

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1081/pde-120025485

zbMATH Keywords

wave propagationRiemannian metricsmaterial propertiesDirichlet-to-Neumann maplinear hyperelastic media

Mathematics Subject Classification ID

Linear elasticity with initial stresses (74B10) Inverse problems for PDEs (35R30) Inverse problems for waves in solid mechanics (74J25)

Related Items

Uniqueness and Stability of Determining the Residual Stress by One Measurement ⋮ Recovery of wave speeds and density of mass across a heterogeneous smooth interface from acoustic and elastic wave reflection operators ⋮ Detecting an inclusion in an elastic body with residual stress ⋮ Stability estimate for the hyperbolic inverse boundary value problem by local Dirichlet-to-Neumann map ⋮ On uniqueness in the inverse problem for transversely isotropic elastic media with a disjoint wave mode ⋮ Unique continuation for the elastic transversely isotropic dynamical systems and its application ⋮ Partial uniqueness and obstruction to uniqueness in inverse problems for anisotropic elastic media ⋮ Uniqueness of the density in an inverse problem for isotropic elastodynamics ⋮ Carleman Estimates with Second Large Parameter for Second Order Operators ⋮ Stability estimate for an inverse problem for the wave equation in a magnetic field ⋮ On Transversely Isotropic Elastic Media with Ellipsoidal Slowness Surfaces ⋮ Conditional Stability for the Hexagonal Anisotropic Elastic Dynamical Systems ⋮ Stability estimate for an inverse problem for the magnetic Schrödinger equation from the Dirichlet-to-Neumann map ⋮ Lipschitz stability for a hyperbolic inverse problem by finite local boundary data

Cites Work

• Unnamed Item
• Asymptotic solutions of oscillatory initial value problems
• On the residual stress possible in an elastic body with material symmetry
• Rigidity for metrics with the same lengths of geodesics
• On the propagation of polarization sets for systems of real principal type
• Well-posed quasi-linear second-order hyperbolic systems with applications to nonlinear elastodynamics and general relativity
• Determining residual stress from boundary measurements: A linearized approach
• Semiglobal boundary rigidity for Riemannian metrics
• Propagation of polarization in elastodynamics with residual stress and travel times
• An inverse problem in elastodynamics: Uniqueness of the wave speeds in the interior
• Positive definiteness of the elasticity tensor of a residually stressed material
• On the traction problem of dead loading in linear elasticity with initial stress
• Asymptotic solutions of the elastic wave equation and reflected waves near boundaries
• On the determination of residual stress in an elastic body
• Exact and asymptotic solutions of the cauchy problem
• Boundary identifiability of residual stress via the Dirichlet to Neumann map
• Hartig's law and linear elasticity with initial stress
• Uniqueness of the density in an inverse problem for isotropic elastodynamics
• Local boundary rigidity of a compact Riemannian manifold with curvature bounded above
• Boundary determination for an inverse problem in elastodynamics
• A Nonuniqueness Theorem for an Inverse Boundary Value Problem in Elasticity