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In this work, we investigate inverse problems of recovering the time-dependent coefficient in the nonlinear transport equation in both cases: two-dimensional Riemannian manifolds and Euclidean space $\mathbb{R}^n$, $n\geq 2$. Specifically,…

Analysis of PDEs · Mathematics 2024-10-02 Ru-Yu Lai , Hanming Zhou

We consider the inverse conductivity problem of identifying embedded objects in unbounded domains. The main tool is a set of special solutions to the Schroedinger equation, the complex spherical waves, which are constructed by a Carleman…

Analysis of PDEs · Mathematics 2009-11-11 Mikko Salo , Jenn-Nan Wang

The solution of the wave equation in a polyhedral domain in $\mathbb{R}^3$ admits an asymptotic singular expansion in a neighborhood of the corners and edges. In this article we formulate boundary and screen problems for the wave equation…

Numerical Analysis · Mathematics 2018-07-17 Heiko Gimperlein , Fabian Meyer , Ceyhun Oezdemir , David Stark , Ernst P. Stephan

This paper aims to combine the advantages of the Jordan-Moore-Gibson-Thompson JMGT equation as an advanced model in nonlinear acoustics with a frequency domain formulation of the forward and inverse problem of acoustic nonlinearity…

Analysis of PDEs · Mathematics 2025-08-05 Barbara Kaltenbacher

We consider the inverse problem of determining the Lam\'{e} parameters and the density of a three-dimensional elastic body from the local time-harmonic Dirichlet-to-Neumann map. We prove uniqueness and Lipschitz stability of this inverse…

Analysis of PDEs · Mathematics 2014-12-12 Elena Beretta , Maarten V. de Hoop , Elisa Francini , Sergio Vessella , Jian Zhai

In this work we establish existence and multiplicity of solutions for elliptic problem with nonlinear boundary conditions under strong resonance conditions at infinity. The nonlinearity is resonance at infinity and the reso- nance phenomena…

Analysis of PDEs · Mathematics 2015-07-30 Alzaki Fadlallah , Edcarlos D. Da Silva

The comparative study of two globally convergent numerical methods for acoustic tomography is carried out in two dimensions. These are the boundary control method and the quasi-reversibility method. The novelty is that in the latter a…

Numerical Analysis · Mathematics 2023-01-18 Michael V. Klibanov , Alexandre A. Timonov

This technical note is a complement to an earlier paper [Benzoni-Gavage \& Rosini, Comput. Math. Appl. 2009], which aims at a deeper understanding of a basic model for propagating phase boundaries that was proved to admit surface waves…

Analysis of PDEs · Mathematics 2015-10-05 Jean-François Coulombel , Sylvie Benzoni-Gavage

Ultrasonic propagation through media with thermal and molecular relaxation can be modeled by third-order in time nonlinear wave-like equations with memory. This paper investigates the asymptotic behavior of a Cauchy problem for such a…

Analysis of PDEs · Mathematics 2020-12-03 Vanja Nikolić , Belkacem Said-Houari

This paper considers the non-linear inverse problem of reconstructing an electric conductivity distribution from the interior power density in a bounded domain. Applications include the novel tomographic method known as acousto-electric…

Optimization and Control · Mathematics 2018-08-29 B. J. Adesokan , Kim Knudsen , Venkateswaran P. Krishnan , Souvik Roy

We study partial data inverse problems for linear and nonlinear parabolic equations with unknown time-dependent coefficients. In particular, we prove uniqueness results for partial data inverse problems for semilinear reaction-diffusion…

Analysis of PDEs · Mathematics 2024-06-04 Ali Feizmohammadi , Yavar Kian , Gunther Uhlmann

We construct a measure-valued branching Markov process associated with a nonlinear boundary value problem, where the boundary condition has a nonlinear pseudo monotone branching mechanism term $-\beta$, which includes as a limit case…

Probability · Mathematics 2018-03-16 Viorel Barbu , Lucian Beznea

In this paper, we consider an acoustic wave transmission problem with mixed boundary conditions of Dirichlet, Neumann, and impedance type. The transmission interfaces may join the domain boundary in a general way independent of the location…

Numerical Analysis · Mathematics 2020-10-07 Sarah Eberle , Francesco Florian , Ralf Hiptmair , Stefan A. Sauter

A mechanism for asymmetric (nonreciprocal) wave transmission is presented. As a reference system, we consider a layered nonlinear, non mirror-symmetric model described by the one-dimensional Discrete Nonlinear Schreodinger equation with…

Pattern Formation and Solitons · Physics 2012-04-12 Stefano Lepri , Giulio Casati

Nonlinear eigenvalue problems arise in a wide range of physical systems, in which system parameters depend on the eigenvalue. Such systems have been proposed to exhibit an extreme sensitivity of their spectra to boundary conditions, which…

Mesoscale and Nanoscale Physics · Physics 2026-04-28 Kota Otsuka , Kazuki Yokomizo

We consider an inverse problem for the compressible Euler's equations in polytropic fluid. We show that by taking active measurements near a particle trajectory one can determine the background flow in a set where pressure waves can…

Analysis of PDEs · Mathematics 2026-04-17 Gunther Uhlmann , Yuchao Yi , Jian Zhai

We consider the inverse Calder\'on problem consisting of determining the conductivity inside a medium by electrical measurements on its surface. Ideally, these measurements determine the Dirichlet-to-Neumann map and, therefore, one usually…

Analysis of PDEs · Mathematics 2017-06-28 Pedro Caro , Andoni Garcia

Classical results of second order parabolic quasi-linear equations always require that the nonlinear terms are controlled by a power of the unknown functions and their first derivatives. We improve the previous results. More precisely, in…

Analysis of PDEs · Mathematics 2022-12-06 Zonglin Jia

In this paper, we consider the inverse scattering problem associated with an inhomogeneous media with a conductive boundary. First, we discuss the inverse conductivity problem of reconstructing the conductivity parameter from scattering…

Analysis of PDEs · Mathematics 2017-12-12 Isaac Harris , Andreas Kleefeld

The inverse problem of determining the cross-sectional area of a human vocal tract during the utterance of a vowel is considered. The frequency-dependent boundary condition at the lips is expressed in terms of the acoustic impedance of a…

Mathematical Physics · Physics 2021-03-16 Tuncay Aktosun , Paul Sacks , Xiao-Chuan Xu