Problem for hyperbolic system of equations having constant coefficients with integral conditions with respect to the time variable
In a domain specified in the form of a Cartesian product of a segment $\left[0,T\right]$ and the space ${\mathbb R}^{p}$, we study a problem with integral conditions with respect to the time variable for hyperbolic system with constant coefficients in a class of almost periodic functions in the spa...
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| Format: | Article |
| Language: | English |
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Vasyl Stefanyk Precarpathian National University
2014-12-01
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| Series: | Karpatsʹkì Matematičnì Publìkacìï |
| Subjects: | |
| Online Access: | https://journals.pnu.edu.ua/index.php/cmp/article/view/1359 |
| _version_ | 1828262586645217280 |
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| author | A.M. Kuz B.Yo. Ptashnyk |
| author_facet | A.M. Kuz B.Yo. Ptashnyk |
| author_sort | A.M. Kuz |
| collection | DOAJ |
| description | In a domain specified in the form of a Cartesian product of a segment $\left[0,T\right]$ and the space ${\mathbb R}^{p}$, we study a problem with integral conditions with respect to the time variable for hyperbolic system with constant coefficients in a class of almost periodic functions in the space variables. A criterion for the unique solvability of this problem and sufficient conditions for the existence of its solution are established. To solve the problem of small denominators arising in the construction of solutions of the posed problem, we use the metric approach. |
| first_indexed | 2024-04-13T03:57:09Z |
| format | Article |
| id | doaj.art-ddeaeec8c17548e3bec83073b74ab356 |
| institution | Directory Open Access Journal |
| issn | 2075-9827 2313-0210 |
| language | English |
| last_indexed | 2024-04-13T03:57:09Z |
| publishDate | 2014-12-01 |
| publisher | Vasyl Stefanyk Precarpathian National University |
| record_format | Article |
| series | Karpatsʹkì Matematičnì Publìkacìï |
| spelling | doaj.art-ddeaeec8c17548e3bec83073b74ab3562022-12-22T03:03:36ZengVasyl Stefanyk Precarpathian National UniversityKarpatsʹkì Matematičnì Publìkacìï2075-98272313-02102014-12-016228229910.15330/cmp.6.2.282-2991359Problem for hyperbolic system of equations having constant coefficients with integral conditions with respect to the time variableA.M. Kuz0B.Yo. Ptashnyk1Institute for Applied Problems of Mechanics and Mathematics, 3b Naukova str., 79060, Lviv, UkraineInstitute for Applied Problems of Mechanics and Mathematics, 3b Naukova str., 79060, Lviv, UkraineIn a domain specified in the form of a Cartesian product of a segment $\left[0,T\right]$ and the space ${\mathbb R}^{p}$, we study a problem with integral conditions with respect to the time variable for hyperbolic system with constant coefficients in a class of almost periodic functions in the space variables. A criterion for the unique solvability of this problem and sufficient conditions for the existence of its solution are established. To solve the problem of small denominators arising in the construction of solutions of the posed problem, we use the metric approach.https://journals.pnu.edu.ua/index.php/cmp/article/view/1359integral conditionssmall denominatorslebesgue measurealmost periodic functionhyperbolic system |
| spellingShingle | A.M. Kuz B.Yo. Ptashnyk Problem for hyperbolic system of equations having constant coefficients with integral conditions with respect to the time variable Karpatsʹkì Matematičnì Publìkacìï integral conditions small denominators lebesgue measure almost periodic function hyperbolic system |
| title | Problem for hyperbolic system of equations having constant coefficients with integral conditions with respect to the time variable |
| title_full | Problem for hyperbolic system of equations having constant coefficients with integral conditions with respect to the time variable |
| title_fullStr | Problem for hyperbolic system of equations having constant coefficients with integral conditions with respect to the time variable |
| title_full_unstemmed | Problem for hyperbolic system of equations having constant coefficients with integral conditions with respect to the time variable |
| title_short | Problem for hyperbolic system of equations having constant coefficients with integral conditions with respect to the time variable |
| title_sort | problem for hyperbolic system of equations having constant coefficients with integral conditions with respect to the time variable |
| topic | integral conditions small denominators lebesgue measure almost periodic function hyperbolic system |
| url | https://journals.pnu.edu.ua/index.php/cmp/article/view/1359 |
| work_keys_str_mv | AT amkuz problemforhyperbolicsystemofequationshavingconstantcoefficientswithintegralconditionswithrespecttothetimevariable AT byoptashnyk problemforhyperbolicsystemofequationshavingconstantcoefficientswithintegralconditionswithrespecttothetimevariable |