A Generalized Solution of an Initial Boundary Value Problem Arising in the Mechanics of Discrete-Continuous Systems
In this paper we define a generalized solution of an initial boundary value problem for a linear system of differential equations with one ordinary differential equation and two partial differential equations (a hybrid system of differential equations). We have proved the existence theorem for a gen...
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| Format: | Article |
| Language: | English |
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Yaroslavl State University
2015-02-01
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| Series: | Моделирование и анализ информационных систем |
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| Online Access: | https://www.mais-journal.ru/jour/article/view/14 |
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| _version_ | 1849688218154303488 |
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| author | E. P. Kubyshkin O. A. Khrebtyugova |
| author_facet | E. P. Kubyshkin O. A. Khrebtyugova |
| author_sort | E. P. Kubyshkin |
| collection | DOAJ |
| description | In this paper we define a generalized solution of an initial boundary value problem for a linear system of differential equations with one ordinary differential equation and two partial differential equations (a hybrid system of differential equations). We have proved the existence theorem for a generalized solution, its uniqueness, the correctness of the problem. An analytical formula for the solution is found. Such a system of differential equations arises in the study of discrete-continuum mechanical systems. |
| format | Article |
| id | doaj-art-295f7380876d4b4a87bda76da1bf46d6 |
| institution | DOAJ |
| issn | 1818-1015 2313-5417 |
| language | English |
| publishDate | 2015-02-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj-art-295f7380876d4b4a87bda76da1bf46d62025-08-20T03:22:04ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172015-02-01191849610.18255/1818-1015-2012-1-84-968A Generalized Solution of an Initial Boundary Value Problem Arising in the Mechanics of Discrete-Continuous SystemsE. P. Kubyshkin0O. A. Khrebtyugova1Ярославский государственный университет им. П.Г. ДемидоваЯрославский государственный университет им. П.Г. ДемидоваIn this paper we define a generalized solution of an initial boundary value problem for a linear system of differential equations with one ordinary differential equation and two partial differential equations (a hybrid system of differential equations). We have proved the existence theorem for a generalized solution, its uniqueness, the correctness of the problem. An analytical formula for the solution is found. Such a system of differential equations arises in the study of discrete-continuum mechanical systems.https://www.mais-journal.ru/jour/article/view/14generalized solutionwell-posedness of the problemdiscrete-continuum mechanical systemstimoshenko beamanalytical solution formula |
| spellingShingle | E. P. Kubyshkin O. A. Khrebtyugova A Generalized Solution of an Initial Boundary Value Problem Arising in the Mechanics of Discrete-Continuous Systems Моделирование и анализ информационных систем generalized solution well-posedness of the problem discrete-continuum mechanical systems timoshenko beam analytical solution formula |
| title | A Generalized Solution of an Initial Boundary Value Problem Arising in the Mechanics of Discrete-Continuous Systems |
| title_full | A Generalized Solution of an Initial Boundary Value Problem Arising in the Mechanics of Discrete-Continuous Systems |
| title_fullStr | A Generalized Solution of an Initial Boundary Value Problem Arising in the Mechanics of Discrete-Continuous Systems |
| title_full_unstemmed | A Generalized Solution of an Initial Boundary Value Problem Arising in the Mechanics of Discrete-Continuous Systems |
| title_short | A Generalized Solution of an Initial Boundary Value Problem Arising in the Mechanics of Discrete-Continuous Systems |
| title_sort | generalized solution of an initial boundary value problem arising in the mechanics of discrete continuous systems |
| topic | generalized solution well-posedness of the problem discrete-continuum mechanical systems timoshenko beam analytical solution formula |
| url | https://www.mais-journal.ru/jour/article/view/14 |
| work_keys_str_mv | AT epkubyshkin ageneralizedsolutionofaninitialboundaryvalueproblemarisinginthemechanicsofdiscretecontinuoussystems AT oakhrebtyugova ageneralizedsolutionofaninitialboundaryvalueproblemarisinginthemechanicsofdiscretecontinuoussystems AT epkubyshkin generalizedsolutionofaninitialboundaryvalueproblemarisinginthemechanicsofdiscretecontinuoussystems AT oakhrebtyugova generalizedsolutionofaninitialboundaryvalueproblemarisinginthemechanicsofdiscretecontinuoussystems |