Initial Value Problems for Wave Equations on Manifolds

被引：0
作者：
Christian Bär
Roger Tagne Wafo
机构：
[1] Universität Potsdam,Institut für Mathematik
[2] University of Douala,Faculty of Science, Department of Mathematics and Computer Science
来源：
Mathematical Physics, Analysis and Geometry | 2015年 / 18卷
关键词：
Wave equation; Globally hyperbolic Lorentz manifold; Cauchy problem; Goursat problem; Finite energy sections; 35L05; 35L15; 58J45;
D O I：
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学科分类号：
摘要：
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 Hörmander.
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