Boundary-Value Problem with Mixed Conditions for Typeless Linear Partial Differential Equations
| Autor: | S. M. Repetylo, B. I. Ptashnyk |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Pure mathematics
Constant coefficients Series (mathematics) General Mathematics 010102 general mathematics Orthogonal functions Cartesian product 01 natural sciences Domain (mathematical analysis) 010101 applied mathematics Stochastic partial differential equation symbols.namesake symbols Boundary value problem 0101 mathematics Mathematics Numerical partial differential equations |
| Zdroj: | Ukrainian Mathematical Journal. 68:756-776 |
| ISSN: | 1573-9376 0041-5995 |
| DOI: | 10.1007/s11253-016-1256-8 |
| Popis: | In the domain obtained as the Cartesian product of a segment 0 ≤ t ≤ T by a p-dimensional torus in the variables x 1 ,…,x p , p ≥ 1, we study the problem with mixed boundary conditions in the variable t for general (no restrictions are imposed on the type) linear partial differential equations of high order with constant coefficients isotropic with respect to the order of differentiation for all independent variables. We establish conditions for the unique solvability of the problem in various functional spaces and construct its solution in the form of a series in systems of orthogonal functions of the variables x 1 ,…,x p . |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|