Geodesic
Cauchy problem for the wave equation on~non-globally hyperbolic manifolds
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2011), pp. 42-46

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We consider Cauchy problem for wave equation on two types of non-global hyperbolic manifolds: Minkowski plane with an attached handle and Misner space. We prove that the classical solution on a plane with a handle exists and is unique if and only if a finite set of point-wise constraints on initial values is satisfied. On the Misner space the existence and uniqueness of a solution is equivalent to much stricter constraints for the initial data.
Keywords: wave equation, Cauchy problem, non-globally hyperbolic manifolds. 
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     author = {O. V. Groshev},
     title = {Cauchy problem for the wave equation on~non-globally hyperbolic manifolds},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {42--46},
     publisher = {mathdoc},
     number = {1},
     year = {2011},
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     url = {http://geodesic.mathdoc.fr/item/VSGTU_2011_1_a5/}
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O. V. Groshev. Cauchy problem for the wave equation on~non-globally hyperbolic manifolds. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2011), pp. 42-46. http://geodesic.mathdoc.fr/item/VSGTU_2011_1_a5/