Seminars: I. A. Ikromov, Sharp time decay estimates for the discrete Klein-Gordon equation

SEMINARS


Seminar on Modern Problems of Complex Analysis (Sadullaev Seminar) May 27, 2021 12:00, Tashkent, National University of Uzbekistan, Room A304 (Department of Mathematics)

Sharp time decay estimates for the discrete Klein-Gordon equation I. A. Ikromov A. Navoi Samarkand State University
Abstract: We establish sharp time decay estimates for the the Klein-Gordon equation on the cubic lattice in dimensions $d = 2, 3, 4$. The $l^1\mapsto l^\infty$ dispersive decay rate is $\|t\|-3/4$ for $d = 2$, $\|t\|-7/6$ for $d = 3$ and $\|t\|-3/2 \log \|t\|$ for $d = 4$. These decay rates are faster than conjectured by Kevrekidis and Stefanov (2005). The proof relies on oscillatory integral estimates and proceeds by a detailed analysis of the the singularities of the associated phase function. We also prove new Strichartz estimates and discuss applications to nonlinear PDEs and spectral theory. Website: https://us02web.zoom.us/j/8022228888