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In this paper, we study the simultaneous controllability of wave systems in an open domain of R d , d $\in$ N *. We obtain a partial controllability result on a co-finite dimensional space for wave equations coupled by a single control…

Analysis of PDEs · Mathematics 2020-12-03 Jingrui Niu

This paper is devoted to a study of observability estimate for the wave equation with variable coefficients $(h^{jk}(x))_{n\times n}$ ($n\in\mathbb{N})$. We consider both the observation point lies outside the domain and the observation…

Analysis of PDEs · Mathematics 2021-12-20 Zhonghua Liao , Xiaoyu Fu

In this paper, we are concerned with the boundary controllability of heat equation with dynamic boundary conditions. More precisely, we prove that the equation is null controllable at any positive time by means of a boundary control…

Analysis of PDEs · Mathematics 2022-06-23 S. E. Chorfi , G. El Guermai , A. Khoutaibi , L. Maniar

We study the controllability of the multidimensional wave equation in a bounded domain with Dirichlet boundary condition, in which the support of the control is allowed to change over time. The exact controllability is reduced to the proof…

Optimization and Control · Mathematics 2018-05-09 Antonio Agresti , Daniele Andreucci , Paola Loreti

Energy decay is established for the damped wave equation on compact Riemannian manifolds where the damping coefficient is allowed to depend on time. Using a time dependent observability inequality, it is shown that the energy of solutions…

Analysis of PDEs · Mathematics 2023-11-14 Perry Kleinhenz

This paper is devoted to study exact controllability of two one-dimensional coupled wave equations with first-order coupling terms with coefficients depending on space and time. We give a necessary and sufficient condition for both exact…

Optimization and Control · Mathematics 2021-11-16 Farid Ammar Khodja , Yacine Mokhtari

In this paper, we consider the inverse boundary problems of recovering the time-dependent nonlinearity and damping term for a semilinear wave equation on a Riemannian manifold. The Carleman estimate and the construction of Gaussian beams…

Analysis of PDEs · Mathematics 2022-12-08 Song-Ren Fu

We prove localized energy estimates for the wave equation in domains with a strictly concave boundary when homogeneous Dirichlet or Neumann conditions are imposed. By restricting the solution to small, frequency dependent, space time…

Analysis of PDEs · Mathematics 2014-11-07 Matthew D. Blair

We discuss admissibility and exact observability estimates of boundary observation and interior point observation of a one-dimensional wave equation on a time dependent domain for sufficiently regular boundary functions. We also discuss…

Analysis of PDEs · Mathematics 2017-05-31 Bernhard Hermann Haak , Duc-Trung Hoang

We consider the stability in the inverse problem consisting of the determination of a time-dependent coefficient of order zero $q$, appearing in a Dirichlet initial-boundary value problem for a wave equation $\partial_t^2u-\Delta…

Analysis of PDEs · Mathematics 2016-02-01 Yavar Kian

We establish a new family of Carleman inequalities for wave operators on cylindrical spacetime domains containing a potential that is critically singular, diverging as an inverse square on all the boundary of the domain. These estimates are…

Analysis of PDEs · Mathematics 2020-03-31 Alberto Enciso , Arick Shao , Bruno Vergara

We study the wave equation in a bounded domain or on a compact Riemannian manifold with boundary. Assume that we are given the hyperbolic Neumann-to-Dirichlet map on the boundary corresponding to physical boundary measurements. We consider…

Analysis of PDEs · Mathematics 2007-08-17 Matias Dahl , Anna Kirpichnikova , Matti Lassas

In this article, we prove a variety of uniqueness results for ultrahyperbolic equations with general space and time dependent lower order terms. We address the problem of determining uniqueness of solutions from boundary data as well as…

Analysis of PDEs · Mathematics 2024-12-04 Vaibhav Kumar Jena

In this paper, we shall prove a Carleman estimate for the so-called Zaremba problem. Using some techniques of interpolation and spectral estimates, we deduce a result of stabilization for the wave equation by means of a linear Neumann…

Analysis of PDEs · Mathematics 2016-04-05 Pierre Cornilleau , Luc Robbiano

Given the wave equation on a compact Riemannian manifold with boundary, we derive an explicit reconstruction procedure to represent the frequency-domain Neumann-to-Dirichlet map in terms of the time-domain Neumann-to-Dirichlet map at any…

Analysis of PDEs · Mathematics 2026-02-17 Yang Yang

We investigate the internal observability of the wave equation with Dirichlet boundary conditions in a triangular domain. More precisely, the domain taken into exam is the half of the equilateral triangle. Our approach is based on Fourier…

Optimization and Control · Mathematics 2018-07-30 Vilmos Komornik , Anna Chiara Lai , Paola Loreti

An approach for shielding an unwanted wave with a fixed frequency by generating a suitably controlled nontrivial wave with the same frequency is suggested. Unlike the well known surface potential approach, the source of the controlled wave…

Analysis of PDEs · Mathematics 2021-07-27 Masaru Ikehata

We prove the interior null-controllability of one-dimensional parabolic equations with time independent measurable coefficients.

Optimization and Control · Mathematics 2007-05-23 G. Alessandrini , L. Escauriaza

This work is concerned with the obtainment of new Carleman estimates for linear parabolic equations, where the second-order differential operator brings a super strong degeneracy in a positive measure subset of the spatial domain. In order…

Analysis of PDEs · Mathematics 2024-04-22 Bruno S. V. Araújo , Reginaldo Demarque , Josiane C. O. Faria , Luiz Viana

We consider the inverse problem for the wave equation on a compact Riemannian manifold or on a bounded domain of $\R^n$, and generalize the concept of {\em domain of influence}. We present an efficient minimization algorithm to compute the…

Analysis of PDEs · Mathematics 2011-01-26 Lauri Oksanen