Existence and uniqueness of classical solutions of the~Cauchy problem on nonglobally hyperbolic manifolds
Teoretičeskaâ i matematičeskaâ fizika, Tome 164 (2010) no. 3, pp. 441-446
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We consider the Cauchy problem for the wave equation on the Misner space, a nonglobally hyperbolic manifold with closed timelike lines. We prove that the existence and uniqueness of a classical solution are equivalent to self-consistency conditions much more rigorous than a finite collection of pointlike conditions occurring in this problem on the Minkowski plane with an attached handle.
Keywords:
nonglobally hyperbolic manifold, wave equation, Cauchy problem.
@article{TMF_2010_164_3_a13,
author = {O. V. Groshev},
title = {Existence and uniqueness of classical solutions of {the~Cauchy} problem on nonglobally hyperbolic manifolds},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {441--446},
publisher = {mathdoc},
volume = {164},
number = {3},
year = {2010},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2010_164_3_a13/}
}
TY - JOUR AU - O. V. Groshev TI - Existence and uniqueness of classical solutions of the~Cauchy problem on nonglobally hyperbolic manifolds JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2010 SP - 441 EP - 446 VL - 164 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2010_164_3_a13/ LA - ru ID - TMF_2010_164_3_a13 ER -
%0 Journal Article %A O. V. Groshev %T Existence and uniqueness of classical solutions of the~Cauchy problem on nonglobally hyperbolic manifolds %J Teoretičeskaâ i matematičeskaâ fizika %D 2010 %P 441-446 %V 164 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_2010_164_3_a13/ %G ru %F TMF_2010_164_3_a13
O. V. Groshev. Existence and uniqueness of classical solutions of the~Cauchy problem on nonglobally hyperbolic manifolds. Teoretičeskaâ i matematičeskaâ fizika, Tome 164 (2010) no. 3, pp. 441-446. http://geodesic.mathdoc.fr/item/TMF_2010_164_3_a13/