Now showing items 1-7 of 7

    • Complexity and regularity of maximal energy domains for the wave equation with fixed initial data 

      Privat Y.; Trélat E.; Zuazua E. (Discrete and Continuous Dynamical Systems- Series A, 2015-12-31)
      We consider the homogeneous wave equation on a bounded open connected subset Ω of IRn. Some initial data being specified, we consider the problem of determining a measurable subset ω of Ω maximizing the L2-norm of the ...
    • Dispersion for 1-d Schrödinger and wave equations with bv coefficients 

      Beli N.; Ignat L.I.; Zuazua E. (Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis, 2016-01-01)
      In this paper we analyze the dispersion for one dimensional wave and Schrödinger equations with BV coefficients. In the case of the wave equation we give a complete answer in terms of the variation of the logarithm of the ...
    • Optimal location of controllers for the one-dimensional wave equation 

      Privat Y.; Trélat E.; Zuazua E. (Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, 2013-12-31)
      In this paper, we consider the homogeneous one-dimensional wave equation defined on (0,π). For every subset ωâŠ[0,π] of positive measure, every T≥2π, and all initial data, there exists a unique control of minimal norm in ...
    • Optimal Observation of the One-dimensional Wave Equation 

      Privat Y.; Trélat E.; Zuazua E. (Journal of Fourier Analysis and Applications, 2013-12-31)
      In this paper, we consider the homogeneous one-dimensional wave equation on [0,π] with Dirichlet boundary conditions, and observe its solutions on a subset ω of [0,π]. Let L∈(0,1). We investigate the problem of maximizing ...
    • Schrödinger operators with boundary singularities: Hardy inequality, Pohozaev identity and controllability results 

      Cazacu C. (Journal of Functional Analysis, 2012-12-31)
      The aim of this paper is two folded. Firstly, we study the validity of a Pohozaev-type identity for the Schrödinger operator A λ:=-δ-λ/|x| 2, λ∈R, in the situation where the origin is located on the boundary of a smooth ...
    • Stabilization of the wave equation on 1-D networks 

      Valein J.; Zuazua E. (SIAM Journal on Control and Optimization, 2009-12-31)
      In this paper we study the stabilization of the wa ve equation on general 1-d networks. For that, we transfer known observability results in the context of control problems of conservative systems (see [R. Dáger and E. ...
    • Time discrete wave equations: Boundary observability and control 

      Zhang X.; Zheng C.; Zuazua E. (Discrete and Continuous Dynamical Systems, 2009-12-31)
      In this paper we study the exact boundary controllability of a trapezoidal time discrete wave equation in a bounded domain. We prove that the projection of the solution in an appropriate filtered space is exactly controllable ...