Dynamics of Partial Differential Equations

Volume 8 (2011)

Number 2

Weighted energy decay for 1D Dirac equation

Pages: 113 – 125

DOI: https://dx.doi.org/10.4310/DPDE.2011.v8.n2.a3

Author

E. A. Kopylova (Institute for Information Transmission Problems RAS, Moscow, Russia)

Abstract

We obtain a dispersive long-time decay in weighted energy norms for solutions of the 1D Dirac equation with generic potential. The decay extends the results obtained by Jensen, Kato and Murata for the Schrödinger equations.

Keywords

dispersion, Dirac equation, relativistic equations, resolvent, spectral representation, weighted spaces, continuous spectrum, Born series, convolution, long-time asymptotics

2010 Mathematics Subject Classification

34L25, 35L10, 47A40, 81U05

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Published 23 June 2011