The smoothness of solutions of the problems with nonlocal multi-point conditions for strictly hyperbolic equations
We consider the problem with nonlocal multi-point boundary conditions for high order in time strictly hyperbolic equation with variable coe±cients in Cartesian product of the time interval and the spatial multidimensional torus. We establish the solvability of this problem in the Sobolev spaces scal...
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| Format: | Article |
| Language: | English |
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Vasyl Stefanyk Precarpathian National University
2009-06-01
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| Series: | Karpatsʹkì Matematičnì Publìkacìï |
| Online Access: | http://journals.pu.if.ua/index.php/cmp/article/view/11/8 |
| _version_ | 1811281143873404928 |
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| author | V. S. Il'kiv |
| author_facet | V. S. Il'kiv |
| author_sort | V. S. Il'kiv |
| collection | DOAJ |
| description | We consider the problem with nonlocal multi-point boundary conditions for high order in time strictly hyperbolic equation with variable coe±cients in Cartesian product of the time interval and the spatial multidimensional torus. We establish the solvability of this problem in the Sobolev spaces scale for almost all (except for the set of a given small measure) vectors of coefficients in the nonlocal conditions. We prove the metric theorem of the lower estimation of small (nonlinear) denominators of the problem. |
| first_indexed | 2024-04-13T01:28:21Z |
| format | Article |
| id | doaj.art-17d2744f967f4e4a8db03127f7f159b9 |
| institution | Directory Open Access Journal |
| issn | 2075-9827 |
| language | English |
| last_indexed | 2024-04-13T01:28:21Z |
| publishDate | 2009-06-01 |
| publisher | Vasyl Stefanyk Precarpathian National University |
| record_format | Article |
| series | Karpatsʹkì Matematičnì Publìkacìï |
| spelling | doaj.art-17d2744f967f4e4a8db03127f7f159b92022-12-22T03:08:35ZengVasyl Stefanyk Precarpathian National UniversityKarpatsʹkì Matematičnì Publìkacìï2075-98272009-06-01114758The smoothness of solutions of the problems with nonlocal multi-point conditions for strictly hyperbolic equationsV. S. Il'kivWe consider the problem with nonlocal multi-point boundary conditions for high order in time strictly hyperbolic equation with variable coe±cients in Cartesian product of the time interval and the spatial multidimensional torus. We establish the solvability of this problem in the Sobolev spaces scale for almost all (except for the set of a given small measure) vectors of coefficients in the nonlocal conditions. We prove the metric theorem of the lower estimation of small (nonlinear) denominators of the problem.http://journals.pu.if.ua/index.php/cmp/article/view/11/8 |
| spellingShingle | V. S. Il'kiv The smoothness of solutions of the problems with nonlocal multi-point conditions for strictly hyperbolic equations Karpatsʹkì Matematičnì Publìkacìï |
| title | The smoothness of solutions of the problems with nonlocal multi-point conditions for strictly hyperbolic equations |
| title_full | The smoothness of solutions of the problems with nonlocal multi-point conditions for strictly hyperbolic equations |
| title_fullStr | The smoothness of solutions of the problems with nonlocal multi-point conditions for strictly hyperbolic equations |
| title_full_unstemmed | The smoothness of solutions of the problems with nonlocal multi-point conditions for strictly hyperbolic equations |
| title_short | The smoothness of solutions of the problems with nonlocal multi-point conditions for strictly hyperbolic equations |
| title_sort | smoothness of solutions of the problems with nonlocal multi point conditions for strictly hyperbolic equations |
| url | http://journals.pu.if.ua/index.php/cmp/article/view/11/8 |
| work_keys_str_mv | AT vsilkiv thesmoothnessofsolutionsoftheproblemswithnonlocalmultipointconditionsforstrictlyhyperbolicequations AT vsilkiv smoothnessofsolutionsoftheproblemswithnonlocalmultipointconditionsforstrictlyhyperbolicequations |