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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2011, Issue 1(22), Pages 42–46 (Mi vsgtu898)  

Procedings of the 2nd International Conference "Mathematical Physics and its Applications"
Mathematical Physics

Cauchy problem for the wave equation on non-globally hyperbolic manifolds

O. V. Groshev

Dept. of Mathematical Physics, Steklov Mathematical Institute, Russian Academy of Sciences, Moscow

Abstract: 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

DOI: https://doi.org/10.14498/vsgtu898

Full text: PDF file (514 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

Document Type: Article
UDC: 517.95
MSC: 35L05
Original article submitted 21/XII/2010
revision submitted – 17/II/2011

Citation: O. V. Groshev, “Cauchy problem for the wave equation on non-globally hyperbolic manifolds”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 1(22) (2011), 42–46

Citation in format AMSBIB
\Bibitem{Gro11}
\by O.~V.~Groshev
\paper Cauchy problem for the wave equation on~non-globally hyperbolic manifolds
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2011
\vol 1(22)
\pages 42--46
\mathnet{http://mi.mathnet.ru/vsgtu898}
\crossref{https://doi.org/10.14498/vsgtu898}
\elib{http://elibrary.ru/item.asp?id=16387157}


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  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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