Geodesic
On Solutions to the Wave Equation on a~Non-globally Hyperbolic Manifold
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Selected topics of mathematical physics and $p$-adic analysis, Tome 265 (2009), pp. 273-287

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We consider the Cauchy problem for the wave equation on a non-globally hyperbolic manifold of special form (the Minkowski plane with a handle) containing closed time-like curves. We prove that the classical solution of the Cauchy problem exists and is unique for initial data satisfying a specific set of additional requirements. 
@article{TM_2009_265_a23,
     author = {I. V. Volovich and O. V. Groshev and N. A. Gusev and E. A. Kuryanovich},
     title = {On {Solutions} to the {Wave} {Equation} on {a~Non-globally} {Hyperbolic} {Manifold}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {273--287},
     publisher = {mathdoc},
     volume = {265},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2009_265_a23/}
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I. V. Volovich; O. V. Groshev; N. A. Gusev; E. A. Kuryanovich. On Solutions to the Wave Equation on a~Non-globally Hyperbolic Manifold. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Selected topics of mathematical physics and $p$-adic analysis, Tome 265 (2009), pp. 273-287. http://geodesic.mathdoc.fr/item/TM_2009_265_a23/