JournalspmVol. 72, No. 4pp. 309–355

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

We prove the time decay estimates L1(R)L(R),L^1 ({\cal R}) \rightarrow L^\infty ({\cal R}), where R{\cal R} is an infinite star-shaped network, for the Schrödinger group eit(d2dx2+V)e^{it(- \frac{d^2}{dx^2} + V)} for real-valued potentials VV 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