The Dirichlet–Neumann problem for linear nonelliptic partial differential equations with constant coefficients

1Ptashnyk, BYo.
1Repetylo, SM
1Ya. S. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of NAS of Ukraine, Lviv
Dopov. Nac. akad. nauk Ukr. 2015, 2:24-31
Section: Mathematics
Language: Ukrainian

In the domain, which is the Cartesian product of a segment and a multidimensional torus, we study the boundary value-problem with Dirichlet-Neumann conditions with respect to the selected variable and conditions of periodicity with respect to other coordinates for general (regardless of type) linear partial differential equations of a high order with constant coefficients, isotropic in the order of differentiation with respect to independent variables. We establish conditions for the unique solvability of the problem and structurally built the solution in the form of a series in a system of orthogonal functions. To estimate the small denominators arising in the construction of a solution to the problem from below, we use the metric approach.

Keywords: constant coefficients, Dirichlet–Neumann problem, linear nonelliptic partial differential equation
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