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We consider inverse problems for wave, heat and Schr\"odinger-type operators and corresponding spectral problems on domains of ${\bf R}^n$ and compact manifolds. Also, we study inverse problems where coefficients of partial differential…

Analysis of PDEs · Mathematics 2007-05-23 Alexander Katchalov , Yaroslav Kurylev , Matti Lassas , Niculae Mandache

We are concerned with isentropic gas flow in the Laval nozzle with a friction due to viscosity. It is well known that the flow attains the sonic state at the throat, where the cross section is minimum in the Laval nozzle. However, the…

Analysis of PDEs · Mathematics 2021-06-02 Naoki Tsuge

In this article, we study the one-dimensional inverse problem of determining the memory kernel by the integral overdetermination condition for the direct problem of finding the velocity potential and the displacement of boundary points. A…

Analysis of PDEs · Mathematics 2026-02-24 Zhanna D. Totieva , Kush Kinra , Manil T. Mohan

We consider an inverse problem of recovering a parameter appearing in all levels in a second-order hyperbolic equation from a single boundary measurement. The model is motivated from applications in photoacoustic tomography when one seeks…

Analysis of PDEs · Mathematics 2024-08-26 Shitao Liu , Gunther Uhlmann , Yang Yang

We study the fixed angle inverse scattering problem of determining a sound speed from scattering measurements corresponding to a single incident wave. The main result shows that a sound speed close to constant can be stably determined by…

Analysis of PDEs · Mathematics 2023-04-25 Shiqi Ma , Leyter Potenciano-Machado , Mikko Salo

In this paper, we consider inverse time-harmonic acoustic and electromagnetic scattering from locally perturbed rough surfaces in three dimensions. The scattering interface is supposed to be the graph of a Lipschitz continuous function with…

Analysis of PDEs · Mathematics 2018-12-24 Yu Zhao , Guanghui Hu , Baoqiang Yan

Thermoacoustic tomography is a term for the inverse problem of determining of one of initial conditions of a hyperbolic equation from boundary measurements. In the past publications both stability estimates and convergent numerical methods…

Mathematical Physics · Physics 2015-06-11 Michael V. Klibanov

We study the inverse problem of recovering the order and the diffusion coefficient of an elliptic fractional partial differential equation from a finite number of noisy observations of the solution. We work in a Bayesian framework and show…

Analysis of PDEs · Mathematics 2017-06-28 Nicolas Garcia Trillos , Daniel Sanz-Alonso

Inverse problems in computational mechanics consist of inferring physical fields that are latent in the model describing some observable fields. For instance, an inverse problem of interest is inferring the Reynolds stress field in the…

Computational Physics · Physics 2020-06-24 Carlos A. Michelén Ströfer , Xinlei Zhang , Heng Xiao , Olivier Coutier-Delgosha

We consider the following inverse problem: Suppose a $(1+1)$-dimensional wave equation on $\mathbb{R}_+$ with zero initial conditions is excited with a Neumann boundary data modelled as a white noise process. Given also the Dirichlet data…

Analysis of PDEs · Mathematics 2026-01-19 Emilia L. K. Blåsten , Tapio Helin , Antti Kujanpää , Lauri Oksanen , Jesse Railo

This work is concerned with an inverse elastic scattering problem of identifying the unknown rigid obstacle embedded in an open space filled with a homogeneous and isotropic elastic medium. A Newton-type iteration method relying on the…

Numerical Analysis · Mathematics 2023-10-13 Yan Chang , Yukun Guo , Hongyu Liu , Deyue Zhang

According to the classical Helmholtz picture, an organ pipe while generating its eigentone has two anti-nodes at the two open ends of a cylinder, the anti-nodes being taken as boundary condition for the corresponding sound. Since 1860 it is…

Sound production due to turbulence is widely shown to be an important phenomenon involved in a.o. fricatives, singing, whispering and speech pathologies. In spite of its relevance turbulent flow is not considered in classical physical…

Classical Physics · Physics 2009-07-24 Xavier Grandchamp , Annemie Van Hirtum , Xavier Pelorson

Assigning homogeneous boundary conditions, such as acoustic impedance, to the thermoviscous wave equations (TWE) derived by transforming the linearized Navier-Stokes equations (LNSE) to the frequency domain yields a so-called Helmholtz…

Computational Physics · Physics 2018-01-09 Danish Patel , Prateek Gupta , Carlo Scalo

We consider an undetermined coefficient inverse problem for a non-\\linear partial differential equation occurring in high intensity ultrasound propagation as used in acoustic tomography. In particular, we investigate the recovery of the…

Analysis of PDEs · Mathematics 2021-02-16 Barbara Kaltenbacher , William Rundell

We consider an inverse problem for the Boltzmann equation on a globally hyperbolic Lorentzian spacetime $(M,g)$ with an unknown metric $g$. We consider measurements done in a neighbourhood $V\subset M$ of a timelike path $\mu$ that connects…

Analysis of PDEs · Mathematics 2022-09-29 Tracey Balehowsky , Antti Kujanpää , Matti Lassas , Tony Liimatainen

We consider the inverse problem of determining different type of information about a diffusion process, described by ordinary or fractional diffusion equations stated on a bounded domain, like the density of the medium or the velocity field…

Analysis of PDEs · Mathematics 2019-07-05 Yavar Kian , Zhiyuan Li , Yikan Liu , Masahiro Yamamoto

We prove a local Lipschitz stability estimate for Gel'fand-Calder\'on's inverse problem for the Schr\"odinger equation. The main novelty is that only a finite number of boundary input data is available, and those are independent of the…

Analysis of PDEs · Mathematics 2020-04-21 Giovanni S. Alberti , Matteo Santacesaria

We consider the inverse problem of determining the density coefficient appearing in the wave equation from separated point source and point receiver data. Under some assumptions on the coefficients, we prove uniqueness results.

Analysis of PDEs · Mathematics 2019-06-24 Manmohan Vashisth

The aim of this paper is to put the problem of vibroacoustic imaging into the mathematical framework of inverse problems (more precisely, coefficient identification in PDEs) and regularization. We present a model in frequency domain, prove…

Analysis of PDEs · Mathematics 2021-09-07 Barbara Kaltenbacher