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Initial value problems for wave equations on manifolds

  • We study the global theory of linear wave equations for sections of vector bundles over globally hyperbolic Lorentz manifolds. We introduce spaces of finite energy sections and show well-posedness of the Cauchy problem in those spaces. These spaces depend in general on the choice of a time function but it turns out that certain spaces of finite energy solutions are independent of this choice and hence invariantly defined. We also show existence and uniqueness of solutions for the Goursat problem where one prescribes initial data on a characteristic partial Cauchy hypersurface. This extends classical results due to Hormander.

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Metadaten
Author details:Christian BärORCiDGND, Roger Tagne Wafo
DOI:https://doi.org/10.1007/s11040-015-9176-7
ISSN:1385-0172
ISSN:1572-9656
Title of parent work (English):Mathematical physics, analysis and geometry : an international journal devoted to the theory and applications of analysis and geometry to physics
Publisher:Springer
Place of publishing:Dordrecht
Publication type:Article
Language:English
Year of first publication:2015
Publication year:2015
Release date:2017/03/27
Tag:Cauchy problem; Finite energy sections; Globally hyperbolic Lorentz manifold; Goursat problem; Wave equation
Volume:18
Issue:1
Number of pages:29
Funding institution:Deutsche Forschungsgemeinschaft [Sonderforschungsbereich 647]; Einstein Foundation Berlin
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Peer review:Referiert
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