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

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.

About the authors

Oleg V Groshev

Steklov Mathematical Institute, Russian Academy of Sciences

Email: groshev@mi.ras.ru
аспирант, отд. математической физики; Математический институт им. В. А. Стеклова РАН; Steklov Mathematical Institute, Russian Academy of Sciences

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