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Seminar of Laboratory of Theory of Functions "Modern Problems of Complex Analysis"
May 27, 2021 12:00–13:00
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Sharp time decay estimates for the discrete Klein-Gordon equation
I. A. Ikromov A. Navoi Samarkand State University
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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
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