English
Related papers

Related papers: Global stability for an inverse problem in soil-st…

200 papers

In horizontally shaken granular material different types of pattern formation have been reported. We want to deal with the convection instability which has been observed in experiments and which recently has been investigated numerically.…

Materials Science · Physics 2007-05-23 Clara Saluena , Thorsten Poeschel

We consider the two-dimensional Kirchhoff-Love plate equation in the context of elasticity modeling the stresses and deformations in thin plates subjected to forces and moments. We establish global recovery of the material parameters like…

Analysis of PDEs · Mathematics 2021-02-12 Sombuddha Bhattacharyya , Tuhin Ghosh

This paper focuses on an inverse problem associated with the plate equation which is derived from models in fluid mechanics and elasticity. We establish the unique identifying results in simultaneously determining both the unknown density…

Analysis of PDEs · Mathematics 2023-01-20 Yixian Gao , Hongyu Liu , Yang Liu

We are interested in the identification of a Generalized Impedance Boundary Condition from the far--fields created by one or several incident plane waves at a fixed frequency. We focus on the particular case where this boundary condition is…

Numerical Analysis · Mathematics 2013-07-23 Laurent Bourgeois , Nicolas Chaulet , Houssem Haddar

In this article, we consider inverse problems of determining a source term and a coefficient of a first-order partial differential equation and prove conditional stability estimates with minimum boundary observation data and relaxed…

Analysis of PDEs · Mathematics 2015-09-02 Fikret Gölgeleyen , Masahiro Yamamoto

The inverse problem method is tested for a class of mean field statistical mechanics models representing a mixture of particles of different species. The robustness of the inversion is investigated for different values of the physical…

Mathematical Physics · Physics 2015-06-12 M. Fedele , C. Vernia , P. Contucci

In this paper, we develop a general approach to prove stability for the non linear second step of hybrid inverse problems. We work with general functionals of the form $\sigma|\nabla u|^p$, $0 < p \leq 1$, where $u$ is the solution of the…

Analysis of PDEs · Mathematics 2015-06-16 Carlos Montalto , Plamen Stefanov

We are interested in an inverse medium problem with internal data. This problem is originated from multi-waves imaging. We aim in the present work to study the well-posedness of the inversion in terms of the boundary conditions. We…

Analysis of PDEs · Mathematics 2018-06-12 Mourad Choulli , Faouzi Triki

We consider a class of inverse problems defined by a nonlinear map from parameter or model functions to the data. We assume that solutions exist. The space of model functions is a Banach space which is smooth and uniformly convex; however,…

Functional Analysis · Mathematics 2015-05-30 Maarten V. de Hoop , Lingyun Qiu , Otmar Scherzer

A novel numerical method for solving inverse scattering problem with fixed-energy data is proposed. The method contains a new important concept: the stability index of the inversion problem. This is a number, computed from the data, which…

Mathematical Physics · Physics 2007-05-23 S. Gutman , A. G. Ramm , W. Scheid

Quantifying the stability of an equilibrium is central in the theory of dynamical systems as well as in engineering and control. A comprehensive picture must include the response to both small and large perturbations, leading to the…

Adaptation and Self-Organizing Systems · Physics 2023-03-08 Philipp C. Böttcher , Benjamin Schäfer , Stefan Kettemann , Carsten Agert , Dirk Witthaut

We establish stability inequalities of an inverse obstacle problem for the magnetic Schr\"odinger equation. We mainly study the problem of reconstructing an unknown function defined on the obstacle boundary from two measurements performed…

Analysis of PDEs · Mathematics 2024-11-26 Mourad Choulli , Hiroshi Takase

In this paper we consider the inverse problem of determining a rigid inclusion inside a thin plate by applying a couple field at the boundary and by measuring the induced transversal displacement and its normal derivative at the boundary of…

Analysis of PDEs · Mathematics 2011-11-03 Antonino Morassi , Edi Rosset , Sergio Vessella

We consider the multi-frequency inverse source problem in the presence of a non-homogeneous medium using passive measurements. Precisely, we derive stability estimates for determining the source from the knowledge of only the imaginary part…

Analysis of PDEs · Mathematics 2024-04-23 Faouzi Triki , Kristoffer Linder-Steinlein , Mirza Karamehmedovic

We study the stability of an inverse problem for the fractional conductivity equation on bounded smooth domains. We obtain a logarithmic stability estimate for the inverse problem under suitable a priori bounds on the globally defined…

Analysis of PDEs · Mathematics 2024-09-10 Giovanni Covi , Jesse Railo , Teemu Tyni , Philipp Zimmermann

We consider the inverse fault friction problem of determining the friction coefficient in the Tresca friction model, which can be formulated as an inverse problem for differential inequalities. We show that the measurements of elastic waves…

Analysis of PDEs · Mathematics 2024-05-03 Maarten V. de Hoop , Matti Lassas , Jinpeng Lu , Lauri Oksanen

Under a convexity assumption on the boundary we solve a local inverse problem, namely we show that the geodesic X-ray transform can be inverted locally in a stable manner; one even has a reconstruction formula. We also show that under an…

Differential Geometry · Mathematics 2012-10-09 Gunther Uhlmann , András Vasy

We establish both Lipschitz and logarithmic stability estimates for an inverse flux problem and subsequently apply these results to an inverse boundary coefficient problem. Furthermore, we demonstrate how the stability inequalities derived…

Analysis of PDEs · Mathematics 2025-11-14 Mourad Choulli , Shuai Lu , Hiroshi Takase

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

This paper aims to investigate the stochastic generalization of the projected deterministic constrained modified Swift-Hohenberg equation. In particular, we prove the global well-posedness and its invariance of Hilbert submanifold i.e. if…

Probability · Mathematics 2025-05-06 Javed Hussain , Saeed Ahmed , Abdul Fatah