Smoothing effect for regularized Schrödinger equation on compact manifolds

• Autores: Lassaad Aloui
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 59, Fasc. 1, 2008, págs. 53-62
• Idioma: inglés
• DOI: 10.1007/bf03191181
• Enlaces
  • Texto completo
• Resumen

  • We prove smoothing effect for solutions of a regularized Schrödinger equation on compact manifolds under the hypothesis of the Geometric control.

• Referencias bibliográficas
  • L. Aloui and M. Khenissi, Stabilisation de l’équation des ondes dans un domaine extérieur, Rev. Math. Iberoamericana 18 (2002), 1–16.
  • C. Bardos, G. Lebeau, and J. Rauch, Sharp sufficient conditions for the observation, control and stabilization of waves from the boundary,...
  • M. Ben-Artzi and A. Devinatz, Regularity and decay of solutions to the Stark evolution equation, J. Funct. Anal. 154 (1998), 501–512.
  • M. Ben-Artzi and S. Klainerman, Decay and regularity for the Schrödinger equation, J. Anal. Math. 58 (1992), 25–37.
  • N. Burq, P. Gérard, and N. Tzvetkov, On nonlinear Schrödinger equations in exterior domain, Ann. Inst. H. Poincaré Anal. Non Linéaire 21 (2004),...
  • N. Burq, Smoothing effect for Schrödinger boundary value problems, Duke Math. J. 123 (2004), 403–427.
  • P. Constantin and J.-C. Saut, Local smoothing properties of dispersive equations, J. Amer. Math. Soc. 1 (1988), 413–439.
  • P. Constantin and J.-C. Saut, Local smoothing properties of Schrödinger equations, Indiana Univ. Math. J. 38 (1989), 791–810.
  • B. Dehman, P. Gérard, and G. Lebeau, Stabilization and control for the non-linear Schrödinger equation on a compact surface, Math. Z. 254...
  • S. Doi, Smoothing effects for Schrödinger evolution equation and global behaviour of geodesic flow, Math. Ann. 318 (2000), 355–389.
  • S. Doi, Remarks on the Cauchy problem for Schrödinger-type equations, Comm. Partial Differential Equations 21 (1996), 163–178.
  • S. Doi, Smoothing effects of Schrödinger evolution groups on Riemannian manifolds, Duke Math. J. 82 (1996), 679–706.
  • R.B. Melrose, Singularities and energy decay in acoustical scattering, Duke Math. J. 46 (1979), 43–59.
  • J. Ralston, Solutions of the wave equation with localized energy, Comm. Pure Appl. Math. 22 (1969), 807–823.
  • J. Rauch, Local decay of scattering solutions of Schrödinger-type equation, J. Funct. Anal. 49 (1982), 10–56.
  • J. Rauch and M. Taylor, Exponential decay of solutions of hyperbolic equations in bounded domains, Indiana Univ. Math. J. 24 (1974), 79–86.
  • M. Reed and B. Simon, Methods of Modern Mathematical Physics I: Functional Analysis, Academic Press, New York-London, 1972.
  • P. Sjölin, Regularity of solutions to Schrödinger equations, Duke Math. J. 55 (1987), 699–715.
  • L. Vega, Schrödinger equations: pointwise convergence to the initial data, Proc. Amer. Math. Soc. 102 (1988), 874–878.