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We present stability estimates for the inverse source problem of the stochastic Helmholtz equation in two and three dimensions by either near-field or far-field data. The random source is assumed to be a microlocally isotropic generalized…

Analysis of PDEs · Mathematics 2024-03-21 Tianjiao Wang , Xiang Xu , Yue Zhao

We consider Euler-Bernoulli operators with real coefficients on the unit interval. We prove the following results: i) Ambarzumyan type theorem about the inverse problems for the Euler-Bernoulli operator. ii) The sharp asymptotics of…

Mathematical Physics · Physics 2014-12-17 Andrey Badanin , Evgeny Korotyaev

This paper concerns the inverse source problems for the time-harmonic elastic and electromagnetic wave equations. The goal is to determine the external force and the electric current density from boundary measurements of the radiated wave…

Analysis of PDEs · Mathematics 2018-08-17 Gang Bao , Peijun Li , Yue Zhao

We prove a stability result in the hybrid inverse problem of recovering the electrical conductivity from partial knowledge of one current density field generated inside a body by an imposed boundary voltage. The region where interior data…

Mathematical Physics · Physics 2016-02-17 Carlos Montalto , Alexandru Tamasan

In this paper we explore solvability of steady-state variational inequalities with multivalued operators. Moreover, we are studying the connections between the class of radially semi-continuous operators with semi-bounded variation and…

funct-an · Mathematics 2008-02-03 O. V. Solonoukha

This article considers a Cauchy problem of Helmholtz equations whose solution is well known to be exponentially unstable with respect to the inputs. In the framework of variational quasi-reversibility method, a Fourier truncation is applied…

Numerical Analysis · Mathematics 2022-08-31 Vo Anh Khoa , Nguyen Dat Thuc , Ajith Gunaratne

In this paper we investigate the action of self-consistent transfer operators (STOs) on Birkhoff cones and give sufficient conditions for stability of their fixed points. Our approach relies on the order preservation properties of STOs that…

Dynamical Systems · Mathematics 2024-11-26 Roberto Castorrini , Stefano Galatolo , Matteo Tanzi

In this paper we investigate direct and inverse problems for time-fractional pseudo-parabolic equations associated with the Jacobi operator. The existence and uniqueness of the solutions are proved. Also, the stability result of the inverse…

Analysis of PDEs · Mathematics 2023-01-03 Bayan Bekbolat , Niyaz Tokmagambetov

We study the stability in the inverse problem of determining the time dependent zeroth-order coefficient $q(t,x)$ arising in the wave equation, from boundary observations. We derive, in dimension $n\geq 2$, a log-type stability estimate in…

Analysis of PDEs · Mathematics 2015-12-09 Ibtissem Ben Aïcha

The inverse spectral problem is studied for the Sturm-Liouville operator with a complex-valued potential and arbitrary entire functions in one of the boundary conditions. We obtain necessary and sufficient conditions for uniqueness, and…

Spectral Theory · Mathematics 2021-09-01 Natalia Bondarenko

We obtain H\"older stability estimates for the inverse Steklov and Calder\'on problems for Schr\"odinger operators corresponding to a special class of $L^2$ radial potentials on the unit ball. These results provide an improvement on earlier…

Analysis of PDEs · Mathematics 2023-11-28 Thierry Daudé , Niky Kamran , François Nicoleau

The operator of double differentiation on a finite interval with Robin boundary conditions perturbed by the composition of a Volterra convolution operator and the differentiation one is considered. We study the inverse problem of recovering…

Spectral Theory · Mathematics 2020-01-28 S. A. Buterin , A. E. Choque Rivero

The paper is devoted to a development of the theory of self-adjoint operators in Krein spaces (J-self-adjoint operators) involving some additional properties arising from the existence of C-symmetries. The main attention is paid to the…

Functional Analysis · Mathematics 2011-01-04 Seppo Hassi , Sergii Kuzhel

We discuss the stability theory and numerical analysis of the Helmholtz equation with variable and possibly non-smooth or oscillatory coefficients. Using the unique continuation principle and the Fredholm alternative, we first give an…

Numerical Analysis · Mathematics 2019-04-18 I. G. Graham , S. A. Sauter

In this work we consider stability of recovery of the conductivity and attenuation coefficients of the stationary Maxwell and Schr\"odinger equations from a complete set of (Cauchy) boundary data. By using complex geometrical optics…

Analysis of PDEs · Mathematics 2015-05-04 Ru-Yu Lai , Victor Isakov , Jenn-Nan Wang

In this work we study the phenomenon of increasing stability in the inverse boundary value problem for the Schr\"odinger equation. This problem was previously considered by Isakov in which he discussed the phenomenon in different ranges of…

Analysis of PDEs · Mathematics 2013-02-06 V Isakov , S Nagayasu , G Uhlmann , J-N Wang

In this paper, we study the inverse spectral problem for the Sturm-Liouville operators on a star-shaped graph, which consists in the recovery of the potentials from specral data or several spectra. The uniform stability of these inverse…

Spectral Theory · Mathematics 2026-01-16 E. E. Chitorkin , N. P. Bondarenko

We study an inverse drift problem for a two-dimensional parabolic equation on the unit square with mixed boundary conditions, where the drift coefficient is recovered from terminal observation data $g=u(\cdot,T)$. A monotone operator is…

Numerical Analysis · Mathematics 2026-04-16 Liuying Zhang , Wenlong Zhang , Zhidong Zhang

In this work, we study the inverse spectral problems for the Sturm-Liouville operators on [0,1] with complex coefficients and a discontinuity at $x=a\in(0,1)$. Assume that the potential on (a,1) and some parameters in the discontinuity and…

Spectral Theory · Mathematics 2025-08-22 Xiao-Chuan Xu , Chuan-Fu Yang , Natalia Pavlovna Bondarenko

We consider the reconstruction of the diffusion and absorption coefficients of the diffusion equation from the internal information of the solution obtained from the first step of the inverse photoacoustic tomography (PAT). In practice, the…

Analysis of PDEs · Mathematics 2021-09-22 Faouzi Triki , Qi Xue