Weighted Energy Decay for 3D Klein-Gordon Equation
A.Komech, E.Kopylova
TL;DR
This paper establishes long-time decay estimates in weighted energy norms for solutions of the 3D Klein-Gordon equation with potential, extending classical results from Schrödinger equations through spectral method modifications.
Contribution
It introduces a modified spectral approach to prove dispersive decay for the 3D Klein-Gordon equation, generalizing Jensen and Kato's techniques to relativistic equations.
Findings
Proves dispersive decay in weighted energy norms for 3D Klein-Gordon solutions.
Extends decay results from Schrödinger to Klein-Gordon equations.
Adapts spectral methods for relativistic wave equations.
Abstract
We obtain a dispersive long-time decay in weighted energy norms for solutions of the 3D Klein-Gordon equation with generic potential. The decay extends the results obtained by Jensen and Kato for the 3D Schredinger equation. For the proof we modify the spectral approach of Jensen and Kato to make it applicable to relativistic equations.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Quantum Mechanics and Non-Hermitian Physics · Spectral Theory in Mathematical Physics