Weighted energy decay for magnetic Klein-Gordon equation
Alexander Komech, Elena Kopylova
TL;DR
This paper establishes long-time decay estimates in weighted energy norms for solutions to the 3D magnetic Klein-Gordon equation, extending previous scalar potential results using advanced spectral and velocity estimates.
Contribution
It develops a spectral theory framework and decay estimates specifically for the magnetic Klein-Gordon equation, broadening the understanding of dispersive decay in magnetic settings.
Findings
Proves dispersive decay in weighted energy norms for 3D magnetic Klein-Gordon solutions.
Extends Jensen and Kato's scalar potential results to magnetic potentials.
Utilizes spectral theory and escape velocity estimates for proof.
Abstract
We obtain a dispersive long-time decay in weighted energy norms for solutions of 3D Klein-Gordon equation with magnetic and scalar potentials. The decay extends the results obtained by Jensen and Kato for the Schroedinger equation with scalar potential. For the proof we develop the spectral theory of Agmon, Jensen and Kato and minimal escape velocities estimates of Hunziker, Sigal and Soffer.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Spectral Theory in Mathematical Physics · Numerical methods in inverse problems