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We consider point sources in hyperbolic equations discretized by finite differences. If the source is stationary, appropriate source discretization has been shown to preserve the accuracy of the finite difference method. Moving point…

Numerical Analysis · Mathematics 2022-01-24 Ylva Ljungberg Rydin , Martin Almquist

This paper is concerned with analysis of electromagnetic wave scattering by an obstacle which is embedded in a two-layered lossy medium separated by an unbounded rough surface. Given a dipole point source, the direct problem is to determine…

Analysis of PDEs · Mathematics 2019-09-04 Peijun Li , Jue Wang , Lei Zhang

Variable order space-fractional diffusion equation derived as an important model to describe complex anomalous diffusion phenomenon. In this article, well-posedness theory has been constructed for equations with the "Dirichlet" or the…

Analysis of PDEs · Mathematics 2016-11-08 Junxiong Jia , Jigen Peng

We consider an inverse boundary value problem for diffusion equations with multiple fractional time derivatives. We prove the uniqueness in determining a number of fractional time-derivative terms, the orders of the derivatives and…

Analysis of PDEs · Mathematics 2019-04-15 Zhiyuan Li , O. Y. Imanuvilov , Masahiro Yamamoto

This paper studies an inverse hyperbolic problem for the wave equation with dynamic boundary conditions. It consists of determining some forcing terms from the final overdetermination of the displacement. First, the Fr\'echet…

Analysis of PDEs · Mathematics 2022-12-28 S. E. Chorfi , G. El Guermai , L. Maniar , W. Zouhair

The problem of recovering acoustic sources, more specifically monopoles, from point-wise measurements of the corresponding acoustic pressure at a limited number of frequencies is addressed. To this purpose, a family of sparse optimization…

Optimization and Control · Mathematics 2021-03-30 Konstantin Pieper , Bao Quoc Tang , Philip Trautmann , Daniel Walter

This article deals with time-fractional diffusion equations with time-dependent singular source term. Whenever the order of the time-fractional derivative is either multi-term, distributed or space-dependent, we prove that the system admits…

Analysis of PDEs · Mathematics 2022-09-07 Yavar Kian , Eric Soccorsi

We consider an inverse source problem for partially coherent light propagating in the Fresnel regime. The data is the coherence of the field measured away from the source. The reconstruction is based on a minimum residue formulation, which…

Given near or far field wave measurements generated by some unknown time- and space-dependent acoustic source, we seek to rapidly determine a domain in space-time, as small as possible, that contains the support of a source radiating these…

Analysis of PDEs · Mathematics 2016-07-07 Armin Lechleiter

We study two new classes of inverse problems for a time-switched system in which a fractional wave equation (with Caputo derivative of order $\alpha \in (1,2)$) governs the dynamics on the interval $[0,a)$, and a fractional diffusion…

Analysis of PDEs · Mathematics 2026-05-26 E. T. Karimov , N. A. Murolimova

We study an initial-boundary value problem of variable-order time-fractional diffusion equations in one space dimension. Based on the wellposedness of the proposed model and the smoothing properties of its solutions, which are shown to be…

Analysis of PDEs · Mathematics 2020-01-08 Xiangcheng Zheng , Jin Cheng , Hong Wang

Consider the inverse random source scattering problem for the two-dimensional time-harmonic elastic wave equation with an inhomogeneous, anisotropic mass density. The source is modeled as a microlocally isotropic generalized Gaussian random…

Analysis of PDEs · Mathematics 2018-12-27 Jianliang Li , Peijun Li

This paper is concerned with inverse source problems for the acoustic wave equation in the full space R^3, where the source term is compactly supported in both time and spatial variables. The main goal is to investigate increasing stability…

Analysis of PDEs · Mathematics 2024-03-14 Chun Liu , Suliang Si , Guanghui Hu , Bo Zhang

The inverse source problem for the radiative transfer equation is considered, with partial data. Here it is shown that under certain smoothness conditions on the scattering and absorption coefficients, one can recover sources supported in a…

Analysis of PDEs · Mathematics 2015-05-28 Mark Hubenthal

In this article, we study an inverse problem consisting in the identification of a space-time dependent source term in the Ginzburg-Landau equation from final-time observations. We adopt a weak-solution framework and analyze Tikhonov's…

Analysis of PDEs · Mathematics 2025-11-11 Roberto Morales , Javier-Ramírez-Ganga

We study the increasing stability of an inverse source problem for the Helmholtz equation from limited-aperture far field data at multiple wave numbers. The measurement data are givenby the far field patterns $u^\infity(\hat{x},k)$ for all…

Analysis of PDEs · Mathematics 2024-03-14 Ibtissem Ben Aïcha , Guanghui Hu , Suliang Si

This article studies an inverse problem for a transmission wave equation, a system where the main coefficient has a variable jump across an internal interface given by the boundary between two subdomains. The main result obtains Lipschitz…

Analysis of PDEs · Mathematics 2024-09-11 L Baudouin , A Imba , A Mercado , A Osses

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

This article presents a mathematical study of the problem of identifying a time-dependent source term in transport processes described by a timefractional parabolic equation, based on noisy time-dependent measurements taken at an arbitrary…

Analysis of PDEs · Mathematics 2026-04-06 Guillermo Federico Umbricht , Diana Rubio

In this paper, we investigate the inverse problem of determining the right-hand side of a subdiffusion equation with a Caputo time derivative, where the right-hand side depends on both time and certain spatial variables. Similar inverse…

Analysis of PDEs · Mathematics 2025-05-08 R. R. Ashurov , O. T. Mukhiddinova