Weighted Energy Decay for 1D Klein–Gordon Equation (original) (raw)

Communications in Partial Differential Equations, 2010

Abstract

We obtain a dispersive long-time decay in weighted energy norms for solutions of the 1D Klein–Gordon equation with generic potential. The decay extends the results obtained by Jensen, Kato and Murata for the equations of Schrödinger's type by the spectral approach. For the proof we modify the approach to make it applicable to relativistic equations.

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