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This paper presents a Finite Element Model Updating framework for identifying heterogeneous material distributions in planar Bernoulli-Euler beams based on a rotation-free isogeometric formulation. The procedure follows two steps: First,…

Computational Engineering, Finance, and Science · Computer Science 2025-10-20 Bartłomiej Łazorczyk , Roger A. Sauer

In this paper we show that the shear modulus $\mu$ of an isotropic elastic body can be stably recovered by the knowledge of one single displacement field whose boundary data can be assigned independently of the unknown elasticity tensor.

Analysis of PDEs · Mathematics 2020-12-29 Giuseppe Di Fazio , Elisa Francini , Fabio Raciti , Sergio Vessella

We analyze a mathematical model of elastic dislocations with applications to geophysics, where by an elastic dislocation we mean an open, oriented Lipschitz surface in the interior of an elastic solid, across which there is a discontinuity…

Analysis of PDEs · Mathematics 2019-11-13 Andrea Aspri , Elena Beretta , Anna L. Mazzucato , Maarten V. de Hoop

We propose in this work a novel iterative direct sampling method for imaging moving inhomogeneities in parabolic problems using boundary measurements. It can efficiently identify the locations and shapes of moving inhomogeneities when very…

Numerical Analysis · Mathematics 2025-11-12 Bangti Jin , Fengru Wang , Jun Zou

Dynamic elastography is a widely used, safe, convenient, and cost-effective method to aid in medical diagnosis. It visualizes the wave field propagating through living tissues and quantitatively determines the wave propagation speed from…

Analysis of PDEs · Mathematics 2026-04-15 Yu Jiang , Ching-Lung Lin , Gen Nakamura

In this paper, we consider an inverse conductivity problem on a bounded domain $\Omega\subset\mathbb{R}^n$, $n\geq2$, also known as Electrical Impedance Tomography (EIT), for the case where unknown impenetrable obstacles are embedded into…

Analysis of PDEs · Mathematics 2021-04-29 Jiaqing Yang

Let $\sigma$ be the scattering relation on a compact Riemannian manifold $M$ with non-necessarily convex boundary, that maps initial points of geodesic rays on the boundary and initial directions to the outgoing point on the boundary and…

Differential Geometry · Mathematics 2007-05-23 Plamen Stefanov , Gunther Uhlmann

We present two applications of the integro-differential volume equation for the eigenstrain, building on Eshelby's inclusion method [15,16], in the contexts of both static and dynamic linear elasticity. The primary objective is to address…

Analysis of PDEs · Mathematics 2025-03-25 Drossos Gintides , Leonidas Mindrinos

We study the inverse boundary value problem of detecting a non-uniform conductivity motivated by pacing-guided ablation in cardiac electrophysiology. At the stationary level, the transmembrane potential $u$ in a region…

Analysis of PDEs · Mathematics 2026-02-13 Elena Beretta , Elisa Francini , Dario Pierotti , Eva Sincich

We prove the incompressible limit of non-isentropic inviscid elastodynamic equations with general initial data in 3D half-space. The deformation tensor is assumed to satisfy the neo-Hookean linear elasticity and degenerates in the normal…

Analysis of PDEs · Mathematics 2024-12-16 Jiawei Wang , Junyan Zhang

In this paper, the elastic Dirichlet-to-Neumann map $\Xi_g$ is studied for the stationary elasticity system in a compact Riemannian manifold $(\Omega,g)$ with smooth boundary $\partial \Omega$. By overcoming methodological difficulties, we…

Analysis of PDEs · Mathematics 2022-05-31 Genqian Liu

We consider a model for elastic dislocations in geophysics. We model a portion of the Earth's crust as a bounded, inhomogeneous elastic body with a buried fault surface, along which slip occurs. We prove well-posedness of the resulting…

Analysis of PDEs · Mathematics 2025-02-07 Andrea Aspri , Elena Beretta , Anna L. Mazzucato

We address the inverse problem of recovering the stiffness tensor and density of mass from the Dirichlet-to-Neumann map. We study the invariance of the Euclidean and Riemannian elastic wave equation under coordinate transformations.…

Analysis of PDEs · Mathematics 2024-08-23 Joonas Ilmavirta , Hjørdis Schlüter

We consider the inverse problem of determining a potential in a semilinear elliptic equation from the knowledge of the Dirichlet-to-Neumann map. For bounded Euclidean domains we prove that the potential is uniquely determined by the…

Analysis of PDEs · Mathematics 2022-02-22 Mikko Salo , Leo Tzou

We are concerned with the inverse problem of recovering a conductive medium body. The conductive medium body arises in several applications of practical importance, including the modeling of an electromagnetic object coated with a thin…

Analysis of PDEs · Mathematics 2020-05-12 Xinlin Cao , Huaian Diao , Hongyu Liu

We investigate theoretically the near-wall region in elastic turbulence of a dilute polymer solution in the limit of large Weissenberg number. As it was established experimentally, elastic turbulence possesses a boundary layer where the…

Fluid Dynamics · Physics 2019-02-20 S. Belan , A. Chernykh , V. Lebedev

Motivated by recent interest in elastic problems in which the target space is non-Euclidean, we study a limit where local rest distances within an elastic body are incompatible, yet close to, distances within the ambient space.…

Analysis of PDEs · Mathematics 2025-10-09 Raz Kupferman , Cy Maor

We investigate global uniqueness for an inverse problem for a nonlocal diffusion equation on domains that are bounded in one direction. The coefficients are assumed to be unknown and isotropic on the entire space. We first show that the…

Analysis of PDEs · Mathematics 2022-11-16 Yi-Hsuan Lin , Jesse Railo , Philipp Zimmermann

We study a strongly coupled system consisting of a parabolic equation and a singular Hamilton-Jacobi equation in one space dimension. This system describes the dynamics of dislocation densities in a material submitted to an exterior applied…

Analysis of PDEs · Mathematics 2009-03-10 H. Ibrahim , M. Jazar , R. Monneau

We study the asymptotic behavior of the solution of an anisotropic, heterogeneous, linearized elasticity problem in a cylinder whose diameter $\epsilon$ tends to zero. The cylinder is assumed to be fixed (homogeneous Dirichlet boundary…

Analysis of PDEs · Mathematics 2007-05-23 Juan Casado-Diaz , Manuel Luna-Laynez , Francois Murat