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The Continuity of Solutions with Respect to a Parameter to Symmetric Hyperbolic Systems

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Pseudo-Differential Operators: Analysis, Applications and Computations

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 213))

Abstract

In the preceding paper the initial problem to the Schrödinger equations and the Dirac equations were studied with electromagnetic potentials depending on a parameter \(\epsilon\geq0.\) It was proved that if electromagnetic potentials converge as \(\epsilon\rightarrow0\), then so do the solutions to the corresponding equations. In the present paper a generalization of the result on the Dirac equations is given to symmetric hyperbolic systems with coefficients depending continuously on a parameter.

Mathematics Subject Classification (2000). Primary: 35L40.

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Correspondence to Wataru Ichinose .

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Ichinose, W. (2011). The Continuity of Solutions with Respect to a Parameter to Symmetric Hyperbolic Systems. In: Rodino, L., Wong, M., Zhu, H. (eds) Pseudo-Differential Operators: Analysis, Applications and Computations. Operator Theory: Advances and Applications(), vol 213. Springer, Basel. https://doi.org/10.1007/978-3-0348-0049-5_13

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