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

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
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References:

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