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, FranceKaïs Ammari
Université de Monastir, TunisiaSerge 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](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-pm-volume-72-issue-4.png&w=3840&q=90)
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