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We study the inverse boundary value problems of determining a potential in the Helmholtz type equation for the perturbed biharmonic operator from the knowledge of the partial Cauchy data set. Our geometric setting is that of a domain whose…

Analysis of PDEs · Mathematics 2020-07-13 Boya Liu

Quantum computation has made considerable progress in the last decade with multiple emerging technologies providing proof-of-principle experimental demonstrations of such calculations. However, these experimental demonstrations of quantum…

Quantum Physics · Physics 2022-09-27 Samudra Dasgupta , Travis S. Humble

Here we are investigating the one dimensional inverse source problem for Helmholtz equation where the source function is compactly supported in our domain. We show that increasing stability possible using multi-frequency wave at the two end…

Analysis of PDEs · Mathematics 2019-09-09 Shahah Almutairi , Ajith Gunaratne

In this paper, extending previous results of \cite{J1}, we obtain pointwise nonlinear stability of periodic traveling reaction-diffusion waves, assuming spectral linearized stability, under nonlocalized perturbations. More precisely, we…

Analysis of PDEs · Mathematics 2016-05-06 Soyeun Jung , Kevin Zumbrun

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

This paper deals with quantitative spectral stability for compact operators acting on $L^2(X,m)$, where $(X,m)$ is a measure space. Under fairly general assumptions, we provide a characterization of the dominant term of the asymptotic…

Analysis of PDEs · Mathematics 2024-07-31 Andrea Bisterzo , Giovanni Siclari

In this article, high frequency stability estimates for the determination of the potential in the Schr\"odinger equation are studied when the boundary measurements are made on slightly more than half the boundary. The estimates reflect the…

Analysis of PDEs · Mathematics 2021-10-19 Anupam Pal Choudhury , Venkateswaran P. Krishnan

We present an algorithm for coherent diffractive imaging with phaseless measurements. It treats the forward model as a combination of coherent and incoherent waves. The algorithm reconstructs absorption and phase contrast that quantifies…

Computational Physics · Physics 2022-08-25 Miguel Moscoso , Alexei Novikov , George Papanicolaou , Chrysoula Tsogka

We study the stability for the direct acoustic scattering problem with sound-hard scatterers with minimal regularity assumptions on the scatterers. The main tool we use for this purpose is the convergence in the sense of Mosco. We obtain…

Analysis of PDEs · Mathematics 2017-02-14 Giorgio Menegatti , Luca Rondi

We consider the stability of position control of traveling waves in reaction-diffusion system as proposed in {[}J. L\"ober, H. Engel, arXiv:1304.2327{]}. Instead of analyzing the controlled reaction-diffusion system, stability is studied on…

Pattern Formation and Solitons · Physics 2014-06-16 Jakob Löber

In this paper, we investigate the stabilization of a locally coupled wave equations with local viscoelastic damping of past history type acting only in one equation via non smooth coefficients. First, using a general criteria of…

Analysis of PDEs · Mathematics 2021-05-12 Mohammad Akil , Haidar Badawi , Serge Nicaise , Ali Wehbe

Quantitative photoacoustic tomography (QPAT) is a recent hybrid imaging modality that couples optical tomography with ultrasound imaging to achieve high resolution imaging of optical properties of scattering media. Image reconstruction in…

Analysis of PDEs · Mathematics 2015-09-02 Tian Ding , Kui Ren , Sarah Vallelian

In this article, we discuss quantitative Runge approximation properties for the acoustic Helmholtz equation and prove stability improvement results in the high frequency limit for an associated partial data inverse problem modelled on…

Analysis of PDEs · Mathematics 2021-01-12 María Ángeles García-Ferrero , Angkana Rüland , Wiktoria Zatoń

We consider fractional diffusion equations and study the stability of the inverse problem of determining the time-dependent parameter in a source term or a coefficient of zero-th order term from observations of the solution at one point in…

Analysis of PDEs · Mathematics 2015-01-09 Kenichi Fujishiro , Yavar Kian

A theory for stabilization of quantum resonances by a mechanism similar to one leading to classical resonances in nonlinear systems is presented. It explains recent surprising experimental results, obtained for cold Cesium atoms when driven…

Chaotic Dynamics · Physics 2009-11-07 Shmuel Fishman , Italo Guarneri , Laura Rebuzzini

This paper deals with an inverse source problem for the $1$D time-fractional diffusion equation by using boundary measurement. The conditional stability in identification of the unknown source term is proved on the basis of the Fourier…

Analysis of PDEs · Mathematics 2016-08-25 Zhiyuan Li

We consider an inverse scattering problem and its near-field approximation at high frequencies. We first prove, for both problems, Lipschitz stability results for determining the low-frequency component of the potential. Then we show that,…

Analysis of PDEs · Mathematics 2012-05-31 Habib Ammari , Hajer Bahouri , David Dos Santos Ferreira , Isabelle Gallagher

In this paper we study the inverse problem of identifying a source or an initial state in a time-fractional diffusion equation from the knowledge of a single boundary measurement. We derive logarithmic stability estimates for both…

Analysis of PDEs · Mathematics 2021-12-22 Yavar Kian , Eric Soccorsi , Faouzi Triki

Conventional wisdom dictates that to image the position of fluorescent atoms or molecules, one should stimulate as much emission and collect as many photons as possible. That is, in this classical case, it has always been assumed that the…

Quantum Physics · Physics 2015-03-18 Guang Hao Low , Theodore J. Yoder , Isaac L. Chuang

This paper concerns the stability on the inverse source scattering problem for the one-dimensional Helmholtz equation in a two-layered medium. We show that the increasing stability can be achieved by using multi-frequency wave field at the…

Analysis of PDEs · Mathematics 2017-09-13 Yue Zhao , Peijun Li