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We consider inverse boundary value problems for the Navier-Stokes equations and the isotropic Lam\'e system in two dimensions. The uniqueness without any smallness assumptions on unknown coefficients, which is called global uniqueness, was…

Analysis of PDEs · Mathematics 2013-09-09 O. Yu. Imanuvilov , M. Yamamoto

Consider two inverse problems for Sturm-Liouville problems on the unit interval. It means that there are two corresponding mappings $F, f$ from a Hilbert space of potentials $H$ into their spectral data. They are called isomorphic if $F$ is…

Mathematical Physics · Physics 2023-01-13 Evgeny Korotyaev

An inverse spectral problem is studied for the matrix Sturm-Liouville operator on a finite interval with the general self-adjoint boundary condition. We obtain a constructive solution based on the method of spectral mappings for the…

Spectral Theory · Mathematics 2020-03-05 Natalia Bondarenko

The inverse scattering problem for Sturm-Liouville operators on the line with a matrix transfer condition at the origin is considered. We show that the transfer matrix can be reconstructed from the eigenvalues and reflection coefficient. In…

Spectral Theory · Mathematics 2017-07-05 Sonja Currie , Marlena Nowaczyk , Bruce Alastair Watson

We consider the inverse boundary value problem for the steady state convection diffusion equation. We prove that a velocity field $V$, is uniquely determined by the Dirichlet-to-Neumann map, when $V \in C^{0,\gamma} (\Omega)$, $2/3< \gamma…

Analysis of PDEs · Mathematics 2014-05-28 Valter Pohjola

In this paper we consider the Sturm-Liouville equation -y"+qy = lambda*y on the half line (0,infinity) under the assumptions that x=0 is a regular singular point and nonoscillatory for all real lambda, and that either (i) q is L_1 near…

Numerical Analysis · Mathematics 2013-03-13 Charles Fulton , David Pearson , Steven Pruess

In this paper, partial inverse problems for the quadratic pencil of Sturm-Liouville operators on a graph with a loop were studied. These problems consist in recovering the pencil coefficients on one edge of the graph (a boundary edge or the…

Spectral Theory · Mathematics 2020-05-12 Natalia P. Bondarenko , Chung-Tsun Shieh

The paper investigates spectral properties of multi-interval Sturm-Liouville operators with distributional coefficients. Constructive descriptions of all self-adjoint and maximal dissipative/accumulative extensions in terms of boundary…

Spectral Theory · Mathematics 2020-04-22 Andrii Goriunov

This paper presents a new approach to the two-interval Sturm-Liouville eigenfunction expansions, based essentially on the method of integral equations. We consider the Sturm-Liouville problem together with two supplementary transmission…

Classical Analysis and ODEs · Mathematics 2013-12-12 K. Aydemir , O. Sh. Mukhtarov

In this paper, we shall derive a spectral matrix method for the approximation of the eigenvalues of (weakly) regular and singular Sturm-Liouville problems in normal form with an unbounded potential at the left endpoint. The method is…

Numerical Analysis · Mathematics 2019-05-07 Cecilia Magherini

We consider spectral problems for the Sturm-Liouville operator with arbitrary complex-valued potential q(x) and degenerate boundary conditions. We solve corresponding inverse problem, and also study the completeness property and the basis…

Spectral Theory · Mathematics 2012-10-19 Alexander Makin

Sturm-Liouville problems are abundant in the numerical treatment of scientific and engineering problems. In the present contribution, we present an efficient and highly accurate method for computing eigenvalues of singular Sturm-Liouville…

Numerical Analysis · Mathematics 2015-07-08 Philippe Gaudreau , Richard Slevinsky , Hassan Safouhi

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 perform the complete group classification in the class of cubic Schr\"odinger equations of the form $i\psi_t+\psi_{xx}+\psi^2\psi^*+V(t,x)\psi=0$ where $V$ is an arbitrary complex-valued potential depending on $t$ and $x$. We construct…

Mathematical Physics · Physics 2007-05-23 Roman O. Popovych , Nataliya M. Ivanova , Homayoon Eshraghi

In many cases, groundwater flow in an unconfined aquifer can be simplified to a one-dimensional Sturm-Liouville model of the form: \begin{equation*} x''(t)+\lambda x(t)=h(t)+\varepsilon f(x(t)),\hspace{.1in}t\in(0,\pi) \end{equation*}…

Analysis of PDEs · Mathematics 2021-03-18 D. Maroncelli , E. Collins

In this article, we prove a uniqueness result for a coefficient inverse problems regarding a wave, a heat or a Schr\"odinger equation set on a tree-shaped network, as well as the corresponding stability result of the inverse problem for the…

Analysis of PDEs · Mathematics 2014-07-22 Lucie Baudouin , Masahiro Yamamoto

We consider inverse boundary value problems for the Schrodinger equations in two dimensions. Within less regular classes of potentials, we establish a conditional stability estimate of logarithmic order. Moreover we prove the uniqueness…

Analysis of PDEs · Mathematics 2017-10-04 E. Blåsten , O. Yu. Imanuvilov , M. Yamamoto

We prove a uniqueness theorem for an inverse boundary value problem for the Maxwell system with boundary data assumed known only in part of the bound- ary. We assume that the inaccessible part of the boundary is either part of a plane, or…

Analysis of PDEs · Mathematics 2009-02-25 Pedro Caro , Petri Ola , Mikko Salo

In the paper, we study an inverse spectral problem for quadratic pencils of the Sturm--Liouville operators with singular coefficients and entire functions in the boundary conditions. We prove that a subspectrum is sufficient for recovering…

Spectral Theory · Mathematics 2022-04-26 Maria Kuznetsova

We consider uniqueness in an inverse Schr\"odinger problem in a bounded domain in $\mathbb{R}^2$ given the Dirichlet-to-Neumann map on part of the boundary. On the remaining boundary we impose a new type of singular boundary condition with…

Analysis of PDEs · Mathematics 2018-09-19 Freddy J. F. Symons