Linear evolution equations with strongly measurable      families and application      to the Dirac equation

Noboru Okazawa; Kentarou Yoshii

doi:10.3934/dcdss.2011.4.723

Article Contents

2011, Volume 4, Issue 3: 723-744. Doi: 10.3934/dcdss.2011.4.723

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Linear evolution equations with strongly measurable families and application to the Dirac equation

Noboru Okazawa^1, and
Kentarou Yoshii^1,

1.
Department of Mathematics, Science University of Tokyo, 1-3 Kagurazaka, Sinjuku-ku, Tokyo 162-8601

Received: March 31, 2009

Revised: September 30, 2009

Published: May 2011

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Abstract

A new existence and uniqueness theorem is established for linear evolution equations of hyperbolic type with strongly measurable coefficients in a separable Hilbert space. The result is applied to the Dirac equation with time-dependent potential.

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Mathematics Subject Classification: Primary: 47D06, 47B44; Secondary: 35L45.

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