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Fuchsian Mild Microfunctions with Fractional Order and their Applications to Hyperbolic Equations

  • Yasuo ChibaEmail author
Chapter
Part of the Operator Theory: Advances and Applications book series (OT, volume 213)

Abstract

Kataoka introduced a concept of mildness in boundary value problems. He defined mild microfunctions with boundary values. This theory has effective results in propagation of singularities of diffraction. Furthermore, Oaku introduced F-mild microfunctions and applied them to Fuchsian partial differential equations. Based on these theories, we introduce Fuchsian mild microfunctions with fractional order. We show the properties of such microfunctions and their applications to partial differential equations of hyperbolic type. By using a fractional coordinate transform and a quantised Legendre transform, degenerate hyperbolic equations are transformed into equations with derivatives of fractional order. We present a correspondence between solutions for the hyperbolic equations and those for the transformed equations.

Keywords

Boundary value problems microlocal analysis hyperbolic equations hyperfunctions F-mildness 

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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.School of Computer Science Tokyo University of TechnologyHachiojiJapan

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