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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

The Maxwell-Bloch system of equations with inhomogeneous broadening is studied, and the local and global well-posedness of the corresponding initial-boundary value problem is established by taking advantage of the integrability of the…

Exactly Solvable and Integrable Systems · Physics 2024-08-02 Gino Biondini , Barbara Prinari , Zechuan Zhang

A major problem in solving multi-waves inverse problems is the presence of critical points where the collected data completely vanishes. The set of these critical points depend on the choice of the boundary conditions, and can be directly…

Analysis of PDEs · Mathematics 2015-11-11 Mourad Choulli , Faouzi Triki

The approach to Lipschitz stability for uniformly parabolic equations introduced by Imanuvilov and Yamamoto in 1998 based on Carleman estimates, seems hard to apply to the case of Grushin-type operators studied in this paper. Indeed, such…

Analysis of PDEs · Mathematics 2013-12-10 Karine Beauchard , Piermarco Cannarsa

This work extends the results of [Garde and Hyv\"onen, Math. Comp. 91:1925-1953] on series reversion for Calder\'on's problem to the case of realistic electrode measurements, with both the internal admittivity of the investigated body and…

Numerical Analysis · Mathematics 2023-07-19 Henrik Garde , Nuutti Hyvönen , Topi Kuutela

A Coefficient Inverse Problem for the radiative transport equation is considered. The globally convergent numerical method, the so-called convexification, is developed. For the first time, the viscosity solution is considered for a boundary…

Numerical Analysis · Mathematics 2023-03-17 Michael V. Klibanov , Jingzhi Li , Zhipeng Yang

We study an inverse problem for the viscoacoustic wave equation, an integro-differential model describing wave propagation in viscoacoustic media with memory in the leading order term. The medium is characterized by a spatially varying…

Analysis of PDEs · Mathematics 2026-03-26 Giovanni Covi , Maarten de Hoop , Mikko Salo

We propose an adaptive finite element method for the solution of a coefficient inverse problem of simultaneous reconstruction of the dielectric permittivity and magnetic permeability functions in the Maxwell's system using limited boundary…

Numerical Analysis · Mathematics 2016-01-26 Larisa Beilina , Samar Hosseinzadegan

We study the well-posedness of the Bayesian inverse problem for scalar hyperbolic conservation laws where the statistical information about inputs such as the initial datum and (possibly discontinuous) flux function are inferred from noisy…

Numerical Analysis · Mathematics 2021-07-23 Siddhartha Mishra , David Ochsner , Adrian M. Ruf , Franziska Weber

This work concerns inverse boundary value problems for the time-harmonic Maxwell's equations on differential $1-$forms. We formulate the boundary value problem on a $3-$dimensional compact and simply connected Riemannian manifold $M$ with…

Analysis of PDEs · Mathematics 2023-03-14 Sean Holman , Vasiliki Torega

We study an inverse problem for a coupled system of semilinear Helmholtz equations where we are interested in reconstructing multiple coefficients in the system from internal data measured in applications such as thermoacoustic imaging. We…

Analysis of PDEs · Mathematics 2023-07-06 Kui Ren , Nathan Soedjak

We study some hybrid inverse problems associated to BVP's for Schr\"odinger and Helmholtz type equations. The inverse problems we consider consist in the determination of coefficients from the knowledge of internal energies. We establish…

Analysis of PDEs · Mathematics 2021-08-23 Mourad Choulli

In the current paper we consider an inverse boundary value problem of electromagnetism in a nonlinear Kerr medium. We show the unique determination of the electromagnetic material parameters and the nonlinear susceptibility parameters of…

Analysis of PDEs · Mathematics 2020-09-15 Yernat M. Assylbekov , Ting Zhou

The theory of inverse scattering is developed to study the initial-value problem for the modified matrix Korteweg-de Vries (mmKdV) equation with the $2m\times2m$ $(m\geq 1)$ Lax pairs under the nonzero boundary conditions at infinity. In…

Exactly Solvable and Integrable Systems · Physics 2020-05-04 Jin-Jie Yang , Shou-Fu Tian , Zhi-Qiang Li

The present manuscript consists of inverse problems for a coupled system of wave equations with potential in $\mathbb{R}^3$. By establishing the fundamental solution to the aforementioned operator, we study the uniqueness aspects of the…

Analysis of PDEs · Mathematics 2026-04-09 Rahul Bhardwaj , Manmohan Vashisth

We consider a partial data inverse problem for a time-dependent convection-diffusion equation on an admissible manifold. We prove that the time-dependent convection term and time-dependent density can be recovered uniquely modulo a known…

Analysis of PDEs · Mathematics 2024-05-03 Rohit Kumar Mishra , Anamika Purohit , Manmohan Vashisth

Convergence and stability results for the inverse Born series [Moskow and Schotland, Inverse Problems, 24:065005, 2008] are generalized to mappings between Banach spaces. We show that by restarting the inverse Born series one obtains a…

Mathematical Physics · Physics 2015-06-03 Patrick Bardsley , Fernando Guevara Vasquez

In this paper, we study the stability of two inverse boundary value problems in an infinite slab with partial data. These problems have been studied by Li and Uhlmann for the case of the Schrodinger equation and by Krupchyk, Lassas and…

Analysis of PDEs · Mathematics 2015-12-01 Pedro Caro , Kaloyan Marinov

We present a new technique for the design of transformation-optics devices based on large-scale optimization to achieve the optimal effective isotropic dielectric materials within prescribed index bounds, which is computationally cheap…

Optics · Physics 2013-06-11 David Liu , Lucas H. Gabrielli , Michal Lipson , Steven G. Johnson

In order to avoid the electron oscillation of the cathode and enhance the work efficiency of a vacuum diode, an approach for analyzing the solutions and complex bifurcation has been proposed and used to determine the optimal trajectory of…

Analysis of PDEs · Mathematics 2025-11-05 Denis Sidorov , Alexander Sinitsyn , Omar Toledo Leguizamón , Liguo Wang