English
Related papers

Related papers: Stability estimates for partial data inverse probl…

200 papers

In this paper, we consider the Stokes equations and we are concerned with the inverse problem of identifying a Robin coefficient on some non accessible part of the boundary from available data on the other part of the boundary. We first…

Analysis of PDEs · Mathematics 2013-05-07 Muriel Boulakia , Anne-Claire Egloffe , Celine Grandmont

We consider an inverse problem arising in corrosion detection. We prove a stability result of logarithmic type for the determination of the corroded portion of the boundary and impedance by two measurements on the accessible portion of the…

Analysis of PDEs · Mathematics 2010-04-14 Eva Sincich

In this paper, we study the phenomenon of increasing stability in the inverse boundary value problems for the biharmonic equation. By considering a linearized form, we obtain an increasing Lipschitz-like stability when k is large.…

Analysis of PDEs · Mathematics 2022-11-08 Xiaomeng Zhao , Ganghua Yuan

We study boundary regularity for the inhomogeneous Dirichlet problem for $2s$-stable operators in generalized H\"older spaces. Moreover, we provide explicit counterexamples that showcase the sharpness of our results. Our approach directly…

Analysis of PDEs · Mathematics 2025-10-02 Florian Grube

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 investigate the increasing stability of the inverse Schr\"{o}dinger potential problem with integer power type nonlinearities at a large wavenumber. By considering the first order linearized system with respect to the unknown potential…

Analysis of PDEs · Mathematics 2024-10-07 Sen Zou , Shuai Lu , Boxi Xu

We study the increasing stability of an inverse source problem for the Helmholtz equation from limited-aperture far field data at multiple wave numbers. The measurement data are givenby the far field patterns $u^\infity(\hat{x},k)$ for all…

Analysis of PDEs · Mathematics 2024-03-14 Ibtissem Ben Aïcha , Guanghui Hu , Suliang Si

Let $\Omega =\omega\times\mathbb R$ where $\omega\subset \mathbb R^2$ be a bounded domain, and $V : \Omega \to\mathbb R$ a bounded potential which is $2\pi$-periodic in the variable $x_{3}\in \mathbb R$. We study the inverse problem…

Analysis of PDEs · Mathematics 2016-02-01 Otared Kavian , Yavar Kian , Eric Soccorsi

We consider the problem of the recovery of a Robin coefficient on a part $\gamma \subset \partial \Omega$ of the boundary of a bounded domain $\Omega$ from the principal eigenvalue and the boundary values of the normal derivative of the…

Analysis of PDEs · Mathematics 2020-07-08 Matteo Santacesaria , Toshiaki Yachimura

In this work we study the inverse boundary value problem of determining the refractive index in the acoustic equation. It is known that this inverse problem is ill-posed. Nonetheless, we show that the ill-posedness decreases when we…

Analysis of PDEs · Mathematics 2011-10-25 Sei Nagayasu , Gunther Uhlmann , Jenn-Nan Wang

In this paper we establish a global Carleman estimate for the fourth order Schr\"odinger equation posed on a $1-d$ finite domain. The Carleman estimate is used to prove the Lipschitz stability for an inverse problem consisting in retrieving…

Analysis of PDEs · Mathematics 2013-12-18 Chuang Zheng

This paper is concerned with inverse source problems for the acoustic wave equation in the full space R^3, where the source term is compactly supported in both time and spatial variables. The main goal is to investigate increasing stability…

Analysis of PDEs · Mathematics 2024-03-14 Chun Liu , Suliang Si , Guanghui Hu , Bo Zhang

Consider the scattering of the two- or three-dimensional Helmholtz equation where the source of the electric current density is assumed to be compactly supported in a ball. This paper concerns the stability analysis of the inverse source…

Analysis of PDEs · Mathematics 2016-07-26 Peijun Li , Ganghua Yuan

We consider Schr\"{o}dinger equations with linearly energy-depending potentials which are compactly supported on the half-line. We first provide estimates of the number of eigenvalues and resonances for such complex-valued potentials under…

Mathematical Physics · Physics 2023-07-28 Evgeny Korotyaev , Andrea Mantile , Dmitrii Mokeev

In this work we study the optimality of increasing stability of the inverse boundary value problem (IBVP) for Schr\"{o}dinger equation. The rigorous justification of increasing stability for the IBVP for Schr\"{o}dinger equation were…

Analysis of PDEs · Mathematics 2023-01-13 Pu-Zhao Kow , Gunther Uhlmann , Jenn-Nan Wang

Inverse nodal problem on diffusion operator is the problem of finding the potential functions and parameters in the boundary conditions by using nodal data. In particular, we solve the reconstruction and stability problems using nodal set…

Spectral Theory · Mathematics 2013-02-19 Emrah Yilmaz , Hikmet Kemaloglu

In this paper we prove the uniqueness and stability in determining a time-dependent nonlinear coefficient $\beta(t, x)$ in the Schr\"odinger equation $(i\partial_t + \Delta + q(t, x))u + \beta u^2 = 0$, from the boundary…

Analysis of PDEs · Mathematics 2023-11-07 Ru-Yu Lai , Xuezhu Lu , Ting Zhou

In this article, we prove a stability estimate going from the Radon transform of a function with limited angle-distance data to the $L^p$ norm of the function itself, under some conditions on the support of the function. We apply this…

Analysis of PDEs · Mathematics 2012-12-17 Pedro Caro , David Dos Santos Ferreira , Alberto Ruiz

Partial inverse problems are studied for Sturm-Liouville operators with a discontinuity. The main results of the paper are local solvability and stability of the considered inverse problems. Our approach is based on a constructive algorithm…

Spectral Theory · Mathematics 2019-06-18 Chuan-Fu Yang , Natalia P. Bondarenko

We investigate an inverse Robin spectral problem for the $p$-Laplace operator on a bounded domain with mixed Dirichlet-Robin boundary conditions. The aim is to identify an unknown Robin coefficient on an inaccessible boundary portion from…

Analysis of PDEs · Mathematics 2026-03-10 Farid Bozorgnia , Olimjon Eshkobilov
‹ Prev 1 3 4 5 6 7 10 Next ›