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.
Author details: | Christian BärORCiDGND, Roger Tagne Wafo |
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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 |