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Spatial problem of Darboux type for one model equation of third order. (English) Zbl 0864.35067
Summary: For a hyperbolic type model equation of third order a Darboux type problem is investigated in a dihedral angle. It is shown that there exists a real number \(\rho_0\) such that for \(\alpha>\rho_0\) the problem under consideration is uniquely solvable in the Fréchet space. In the case where the coefficients are constants, Bochner’s method is developed in multi-dimensional domains, and used to prove the unique solvability of the problem both in Fréchet and in Banach spaces.

35L35 Initial-boundary value problems for higher-order hyperbolic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
dihedral angle
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