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This paper provides an analysis of the linearized inverse problem in multifrequency electrical impedance tomography. We consider an isotropic conductivity distribution with a finite number of unknown inclusions with different frequency…

Numerical Analysis · Mathematics 2016-10-06 Giovanni S. Alberti , Habib Ammari , Bangti Jin , Jin-Keun Seo , Wenlong Zhang

We consider two phaseless inverse problems for elliptic equation. The statements of these problems differ from have considered. Namely, instead of given information about modulus of scattering waves, we consider the information related to…

Analysis of PDEs · Mathematics 2018-01-31 V. G. Romanov , M. Yamamoto

In this work, we investigate the dynamic behavior and the topological properties of quasiperiodic elastic metasurfaces, namely arrays of mechanical oscillators arranged over the free surface of an elastic half-space according to a…

Applied Physics · Physics 2022-07-05 Xingbo Pu , Antonio Palermo , Alessandro Marzani

This paper concerns an inverse boundary value problem of recovering a zeroth order time-dependent term of a semi-linear wave equation on a globally hyperbolic Lorentzian manifold. We show that an unknown potential $q$ in the non-linear wave…

Analysis of PDEs · Mathematics 2025-05-14 Matti Lassas , Tony Liimatainen , Leyter Potenciano-Machado , Teemu Tyni

The path-following scheme in [Loisel and Maxwell, SIAM J. Matrix Anal. Appl., 39-4 (2018), pp. 1726-1749] is adapted to efficiently calculate the dispersion relation curve for linear surface waves on an arbitrary vertical shear current.…

Numerical Analysis · Mathematics 2019-05-09 Peter Maxwell , Simen Å Ellingsen

The existence of a two-partial Rayleigh wave coupled to an electrical field in 2mm piezoelectric crystals is known but has rarely been investigated analytically. It turns out that the Z-cut, X-propagation problem can be fully solved, up to…

Soft Condensed Matter · Physics 2013-04-24 Bernard Collet , Michel Destrade

This paper is concerned with the classical inverse scattering problem to recover the refractive index of a medium given near or far field measurements of scattered time-harmonic acoustic waves. It contains the first rigorous proof of…

Numerical Analysis · Mathematics 2015-06-19 Thorsten Hohage , Frederic Weidling

This work considers the propagation of high-frequency waves in highly-scattering media where physical absorption of a nonlinear nature occurs. Using the classical tools of the Wigner transform and multiscale analysis, we derive semilinear…

Analysis of PDEs · Mathematics 2025-04-23 Joseph Kraisler , Wei Li , Kui Ren , John C. Schotland , Yimin Zhong

The effects of velocity shear on the unstable modes driven by the effective gravity (Rayleigh-Taylor and interchange) and resistive drift wave instabilities for inhomogeneous equilibrium fluid/plasma density are analyzed for the localized…

Plasma Physics · Physics 2020-02-19 Yanzeng Zhang , S. I. Krasheninnikov , A. I. Smolyakov

In the present paper we describe a method for solving inverse problems for the Helmholtz equation in radially-symmetric domains given multi-frequency data. Our approach is based on the construction of suitable trace formulas which relate…

Numerical Analysis · Mathematics 2023-10-16 Abinand Gopal , Jeremy Hoskins , Vladimir Rokhlin

We consider an inverse problem for a Westervelt type nonlinear wave equation with fractional damping. This equation arises in nonlinear acoustic imaging, and we show the forward problem is locally well-posed. We prove that the smooth…

Analysis of PDEs · Mathematics 2023-08-01 Li Li , Yang Zhang

General equations describing shear displacements in incompressible hyperelastic materials, holding for an arbitrary form of strain energy density function, are presented and applied to the description of nonlinear Love-type waves…

Exactly Solvable and Integrable Systems · Physics 2026-03-20 Shawn Samuel Carl McAdam , Samuel Opoku Agyemang , Alexei Cheviakov

This paper extends current knowledge on electromagnetic wave scattering from bounded moving media in several regards. First, it complements the usual dispersion relation of moving media, $\omega(\theta_\mathbf{k})$ ($\theta_\mathbf{k}$:…

Optics · Physics 2021-05-04 Zoé-Lise Deck-Léger , Xuezhi Zheng , Christophe Caloz

An inverse boundary value problem for the 1+1 dimensional wave equation $(\partial_t^2 - c(x)^2 \partial_x^2)u(x,t)=0,\quad x\in\mathbb{R}_+$ is considered. We give a discrete regularization strategy to recover wave speed $c(x)$ when we are…

Analysis of PDEs · Mathematics 2018-03-29 Jussi Korpela , Matti Lassas , Lauri Oksanen

We give a rigorous version of the classical Balian-Bloch trace formula, a semiclassical expansion around a periodic reflecting ray of the (regularized) resolvent of the Dirichlet Laplacian on a bounded smooth plane domain. It is equivalent…

Spectral Theory · Mathematics 2015-06-26 Steve Zelditch

This paper is devoted to the algorithmic development of inverse elastic scattering problems. We focus on reconstructing the locations and shapes of elastic scatterers with known dictionary data for the nearly incompressible materials. The…

Analysis of PDEs · Mathematics 2017-11-02 Li Jingzhi , Liu Hongyu , Sun Hongpeng

We investigate the asymptotic relation between the inverse problems relying on the Helmholtz equation and the radiative transfer equation (RTE) as physical models, in the high-frequency limit. In particular, we evaluate the asymptotic…

Numerical Analysis · Mathematics 2022-08-10 Shi Chen , Zhiyan Ding , Qin Li , Leonardo Zepeda-Núñez

This paper is concerned with uniqueness, phase retrieval and shape reconstruction methods for inverse elastic scattering problems with phaseless far field data. Systematically, we study two basic models, i.e., inverse scattering of plane…

Analysis of PDEs · Mathematics 2020-01-08 Xia Ji , Xiaodong Liu

This paper concerns the inverse spectral problem for analytic simple surfaces of revolution. By `simple' is meant that there is precisely one critical distance from the axis of revolution. Such surfaces have completely integrable geodesic…

Mathematical Physics · Physics 2007-05-23 Steve Zelditch

This paper is concerned with pulsating waves for multi-dimensional reaction-diffusion equations in spatially periodic media. First, assuming the existence of pulsating waves connecting two linearly stable steady states, we study the…

Analysis of PDEs · Mathematics 2022-08-16 Weiwei Ding , Zhanghua Liang , Wenfeng Liu