Semi-global solutions to the Goursat problem for second-order hyper-quasilinear hyperbolic systems with lineary dependent principal coefficients and applications to the vacuum Einstein equations

Mathematics > Analysis of PDEs Title:Semi-global solutions to the Goursat problem for second-order hyper-quasilinear hyperbolic systems with lineary dependent principal coefficients and applications to the vacuum Einstein equations View PDF HTML (experimental)Abstract:In this work, we significantly extend the results of D. Houpa, 2006 on the Goursat problem for second-order semi-linear hyperbolic systems to the broader framwork of second-order hyper-quasilinear hyperbolic systems of Goursat type, in which the coefficients of the second-order derivatives depend linearly on the unknown. By adapting techniques inspired by Y. Foures (Choquet)- Bruhat, Acta Mathematica, 1952. we show that in the Sobolev type spaces for the Goursat problem quasilinear hyperbolic of the second order considered, the solution exists and is defined in the vicinity of the meeting characteristic hypersurfaces which carry the initial data. As an application, in harmonic gauge, we derive a semi-global existence and uniqueness result for the vacuum Einstein equations. Current browse context: Bibliographic and Citation Tools Code, Data and Media Associated with this Article Demos Recommenders and Search Tools arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.