Dispersive effects and high frequency behaviour for the Schrödinger equation in star-shaped networks

  • Felix Ali Mehmeti

    Université de Valenciennes et du Hainaut Cambrésis, Valenciennes, France
  • Kaïs Ammari

    Université de Monastir, Tunisia
  • Serge Nicaise

    Université de Valenciennes et du Hainaut Cambrésis, Valenciennes, France

Abstract

We prove the time decay estimates where is an infinite star-shaped network, for the Schrödinger group for real-valued potentials satisfying some regularity and decay assumptions. Further we show that the solution for initial conditions with a lower cutoff frequency tends to the free solution, if the cutoff frequency tends to infinity.

Cite this article

Felix Ali Mehmeti, Kaïs Ammari, Serge Nicaise, Dispersive effects and high frequency behaviour for the Schrödinger equation in star-shaped networks. Port. Math. 72 (2015), no. 4, pp. 309–355

DOI 10.4171/PM/1970