Mixed initial-boundary value problems for second order hyperbolic equations. (English) Zbl 0661.35055

Eskin, Gregory

Commun. Partial Differ. Equations 12, 503-587 (1987).

This paper describes results on well posedness and propagation of singularities for solutions of mixed initial boundary value problems for second order hyperbolic equations in a cylinder \(\Omega ={\mathbb{R}}\times G\) whose boundary \(\partial \Omega\) is divided into two parts \(\Gamma_ 1\), \(\Gamma_ 2\) such that \({\bar \Gamma}{}_ 1\cap {\bar \Gamma}_ 2=\Gamma_ 0\) is a smooth (n-1) dimensional surface and the boundary conditions are given on \(\Gamma_ 1\) and \(\Gamma_ 2\). This gives a more complicated picture of propagation of singularities compared with the usual mixed problem.

Reviewer: C.Zuily

MSC:

35L15	Initial value problems for second-order hyperbolic equations
35L20	Initial-boundary value problems for second-order hyperbolic equations
35B40	Asymptotic behavior of solutions to PDEs
58J47	Propagation of singularities; initial value problems on manifolds
35A20	Analyticity in context of PDEs

Keywords:

well posedness; propagation of singularities; mixed initial boundary value problems

References:

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