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

TitleThe Dirichlet–Neumann problem for linear nonelliptic partial differential equations with constant coefficients
Publication TypeJournal Article
Year of Publication2015
AuthorsPtashnyk, BYo., Repetylo, SM
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
DOI10.15407/dopovidi2015.02.024
Issue2
SectionMathematics
Pagination24-31
Date Published2/2015
LanguageUkrainian
Abstract

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.
Keywordsconstant coefficients, Dirichlet–Neumann problem, linear nonelliptic partial differential equation
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