Boundary-value problem with mixed conditions for linear typeless partial differential equations
In the domain obtained as the Cartesian product of a segment $0 \leq t \leq T$ by a $p$-dimensional torus in variables $x_1, ..., x_p$, $p \geq 1$, we study the problem with mixed boundary conditions in the variable $t$ for general (no restrictions are imposed on the type) linear partial differen...
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| Дата: | 2016 |
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| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Українська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2016
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/1870 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | In the domain obtained as the Cartesian product of a segment $0 \leq t \leq T$ by a $p$-dimensional torus in variables $x_1, ..., x_p$, $p \geq 1$, 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 with respect to systems of orthogonal functions of the
variables $x_1, ..., x_p$. |
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