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Wave Equations on Non-smooth Space-times

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Evolution Equations of Hyperbolic and Schrödinger Type

Part of the book series: Progress in Mathematics ((PM,volume 301))

Abstract

We consider wave equations on Lorentzian manifolds in case of low regularity. We first extend the classical solution theory to prove global unique solvability of the Cauchy problem for distributional data and righthand side on smooth globally hyperbolic space-times. Then we turn to the case where the metric is non-smooth and present a local as well as a global existence and uniqueness result for a large class of Lorentzian manifolds with a weakly singular, locally bounded metric in Colombeau’s algebra of generalized functions.

Mathematics Subject Classification. Primary: 58J45; Secondary: 35L05, 35L15, 35D99, 46F30.

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Authors and Affiliations

  1. Faculty of Mathematics, University of Vienna, Nordbergstraße 15, A-1090, Wien, Austria

    Günther Hörmann, Michael Kunzinger & Roland Steinbauer

Authors
  1. Günther Hörmann
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  2. Michael Kunzinger
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  3. Roland Steinbauer
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Corresponding author

Correspondence to Günther Hörmann .

Editor information

Editors and Affiliations

  1. , Department of Mathematics, Imperial College London, 180 Queen's Gate, London, SW7 2AZ, United Kingdom

    Michael Ruzhansky

  2. , Graduate School of Mathematics, Nagoya University, Furocho, Chikusaku, Nagoya, 464-8602, Japan

    Mitsuru Sugimoto

  3. , Fachbereich Mathematik, Universität Stuttgart, Pfaffenwaldring 57, Stuttgart, 70569, Germany

    Jens Wirth

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Hörmann, G., Kunzinger, M., Steinbauer, R. (2012). Wave Equations on Non-smooth Space-times. In: Ruzhansky, M., Sugimoto, M., Wirth, J. (eds) Evolution Equations of Hyperbolic and Schrödinger Type. Progress in Mathematics, vol 301. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0454-7_9

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