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We present a set of well-posed constraint-preserving boundary conditions for a first-order in time, second-order in space, harmonic formulation of the Einstein equations. The boundary conditions are tested using robust stability, linear and…

General Relativity and Quantum Cosmology · Physics 2008-11-26 Jennifer Seiler , Bela Szilagyi , Denis Pollney , Luciano Rezzolla

In this article, we provide a modified argument for proving conditional stability for inverse problems of determining spatially varying functions in evolution equations by Carleman estimates. Our method needs not any cut-off procedures and…

Analysis of PDEs · Mathematics 2020-12-30 X. Huang , O. Yu. Imanuvilov , M. Yamamoto

We show the existence of a local stable manifold for a bidirectional discrete-time nondiffeomorphic nonlinear Hamiltonian dynamics. This is the case where zero is a closed loop eigenvalue and therefore the Hamiltonian matrix is not…

Optimization and Control · Mathematics 2007-05-23 Carmeliza Navasca

The purpose of this paper is to investigate the stabilization of a one-dimensional coupled wave equations with non smooth localized viscoelastic damping of Kelvin-Voigt type and localized time delay. Using a general criteria of…

Analysis of PDEs · Mathematics 2020-07-17 Mohammad Akil , Haidar Badawi , Ali Wehbe

Motivated by various applications, this article develops the notion of boundary control for Maxwell's equations in the frequency domain. Surface curl is shown to be the appropriate regularization in order for the optimal control problem to…

Optimization and Control · Mathematics 2022-10-03 Harbir Antil , Hugo Díaz

In this article, for the radiative transport equation, we study inverse problems of determining a time independent scattering coefficient or total attenuation by boundary data on the complementary sub-boundary after making one time input of…

Analysis of PDEs · Mathematics 2013-07-30 Manabu Machida , Masahiro Yamamoto

We study both the topological structure stability and the relations of the steady Magnetohydrodynamic equations when $\nu,\eta$ are given different values in muti-connected bounded domain. We also show the solutions's existence for fixed…

Analysis of PDEs · Mathematics 2020-09-22 Xixia Ma

We consider the inverse problem of recovering stationary coefficients in a class of dynamical Schr\"odinger equations with locally analytic nonlinear terms. Upon treating the well-posedness for small initial data and trivial boundary data,…

Analysis of PDEs · Mathematics 2025-08-28 Pranav Arrepu , Hanming Zhou

We prove a stability result in the hybrid inverse problem of recovering the electrical conductivity from partial knowledge of one current density field generated inside a body by an imposed boundary voltage. The region where interior data…

Mathematical Physics · Physics 2016-02-17 Carlos Montalto , Alexandru Tamasan

The possibility of the existence of quasi-stationary electromagnetic fields in plasma supported by their own self-consistent current follows from Maxwell's equations with field sources. These equations also give rise to a wave equation for…

Classical Physics · Physics 2023-01-02 Yurii A. Spirichev

We consider the inverse problem for the wave equation which consists of determining an unknown space-dependent force function acting on a vibrating structure from Cauchy boundary data. Since only boundary data are used as measurements, the…

Numerical Analysis · Mathematics 2014-10-24 S. O. Hussein , D. Lesnic

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

We study the stable behaviour of discrete dynamical systems where the map is convex and monotone with respect to the standard positive cone. The notion of tangential stability for fixed points and periodic points is introduced, which is…

Dynamical Systems · Mathematics 2011-06-20 Marianne Akian , Stephane Gaubert , Bas Lemmens

We study the boundary rigidity problem with partial data consisting of determining locally the Riemannian metric of a Riemannian manifold with boundary from the distance function measured at pairs of points near a fixed point on the…

Differential Geometry · Mathematics 2015-10-09 Plamen Stefanov , Gunther Uhlmann , Andras Vasy

We prove area inequalities for stable marginally outer trapped surfaces in Einstein-Maxwell-dilaton theory. Our inspiration comes on the one hand from a corresponding upper bound for the area in terms of the charges obtained recently by…

General Relativity and Quantum Cosmology · Physics 2015-09-01 David Fajman , Walter Simon

In this paper we investigate the inverse problem of determining the time independent scalar potential of the dynamic Schr\"odinger equation in an infinite cylindrical domain, from partial measurement of the solution on the boundary. Namely,…

Analysis of PDEs · Mathematics 2015-07-27 Mourad Bellassoued , Yavar Kian , Eric Soccorsi

We study linear damped and viscoelastic wave equations evolving on a bounded domain. For both models, we assume that waves are subject to an inhomogeneous Neumann boundary condition on a portion of the domain's boundary. The analysis of…

Analysis of PDEs · Mathematics 2024-10-15 Türker Özsarı , İdem Susuzlu

In this paper we consider a system coupling a wave equation with a heat equation through its boundary conditions. The existence of a small parameter in the heat equation, as a factor multiplying the time derivative, implies the existence of…

Analysis of PDEs · Mathematics 2023-06-06 Gonzalo Arias , Eduardo Cerpa , Swann Marx

We consider the time-harmonic Maxwell equations at a nonzero wavenumber $k\in\mathbb{C}$ on a bounded and simply connected Lipschitz domain $\Omega$ with an analytic boundary $\Gamma$, on which we impose impedance boundary conditions. We…

Analysis of PDEs · Mathematics 2026-03-18 Jens Markus Melenk , David Wörgötter

In this paper we study the stability problem of a tree of elastic strings with local Kelvin-Voigt damping on some of the edges. Under the compatibility condition of displacement and strain and continuity condition of damping coefficients at…

Analysis of PDEs · Mathematics 2018-03-21 Kaïs Ammari , Zhuangyi Liu , Farhat Shel