Advertisement

Observability of a Ring Shaped Membrane via Fourier Series

  • Vilmos Komornik
  • Paola Loreti
  • Michel Mehrenberger
Conference paper
Part of the IFIP Advances in Information and Communication Technology book series (IFIPAICT, volume 494)

Abstract

We study the inverse Ingham type inequality for a wave equation in a ring. This leads to a conjecture on the zeros of Bessel cross product functions. We motivate the validity of the conjecture through numerical results. We do a complete analysis in the particular case of radial initial data, where an improved time of observability is available.

References

  1. 1.
    Abramowitz, M., Stegun, I.A. (eds.): Handbook of Mathematical Functions. Dover, New York (1972)MATHGoogle Scholar
  2. 2.
    Bardos, C., Lebeau, G., Rauch, J.: Sharp suffcient conditions for the observation, control and stabilization of waves from the boundary. SIAM J. Control Optim. 30, 1024–1065 (1992)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
  4. 4.
    Gottlieb, H.P.W.: Eigenvalues of the Laplacian with Neumann boundary conditions. J. Austr. Math. Soc. Ser. B 24, 435–438 (1983)CrossRefMATHGoogle Scholar
  5. 5.
    Haraux, A.: Séries lacunaires et contrôle semi-interne des vibrations d’une plaque rectangulaire. J. Math. Pures Appl. 68, 457–465 (1989)MathSciNetMATHGoogle Scholar
  6. 6.
    Ingham, A.E.: Some trigonometrical inequalities with applications in the theory of series. Math. Z. 41, 367–379 (1936)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Komornik, V., Loreti, P.: Fourier Series in Control Theory. Springer, Heidelberg (2005)MATHGoogle Scholar
  8. 8.
    Lebedev, N.N., Skalskaya, I.P., Uflyand, Y.S.: Worked Problems in Applied Mathematics, Problem 121. Dover, New York (1979)Google Scholar

Copyright information

© IFIP International Federation for Information Processing 2016

Authors and Affiliations

  • Vilmos Komornik
    • 1
  • Paola Loreti
    • 2
  • Michel Mehrenberger
    • 1
  1. 1.Université de StrasbourgStrasbourgFrance
  2. 2.Dipartimento di Scienze di Base e Applicate per l’IngegneriaSapienza Università di RomaRomaItaly

Personalised recommendations