On problem of nonexistence of dissipative estimate for discrete kinetic equations
The existence of a global solution to the discrete kinetic equations in Sobolev spaces is proved, its decomposition by summability is obtained, the influence of its oscillations generated by the interaction operator is explored. The existence of a submanifold ${\mathcal M}_{diss}$ of initial data $(...
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| Format: | Article |
| Language: | English |
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Samara State Technical University
2013-12-01
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| Series: | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
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| Online Access: | https://journals.eco-vector.com/1991-8615/article/viewFile/34699/23050 |
| _version_ | 1811330250084188160 |
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| author | Evgenii Vladimirovich Radkevich |
| author_facet | Evgenii Vladimirovich Radkevich |
| author_sort | Evgenii Vladimirovich Radkevich |
| collection | DOAJ |
| description | The existence of a global solution to the discrete kinetic equations in Sobolev spaces is proved, its decomposition by summability is obtained, the influence of its oscillations generated by the interaction operator is explored. The existence of a submanifold ${\mathcal M}_{diss}$ of initial data $(u^0, v^0, w^0)$ for which the dissipative solution exists is proved. It’s shown that the interaction operator generates the solitons (progressive waves) as the nondissipative part of the solution when the initial data $(u^0, v^0, w^0)$ deviate from the submanifold ${\mathcal M}_{diss}$. The amplitude of solitons is proportional to the distance from $(u^0, v^0, w^0)$ to the submanifold ${\mathcal M}_{diss}$. It follows that the solution can stabilize as $t\to\infty$ only on compact sets of spatial variables. |
| first_indexed | 2024-04-13T15:58:31Z |
| format | Article |
| id | doaj.art-147477fb053e41b4b3e3e3e94af09306 |
| institution | Directory Open Access Journal |
| issn | 1991-8615 2310-7081 |
| language | English |
| last_indexed | 2024-04-13T15:58:31Z |
| publishDate | 2013-12-01 |
| publisher | Samara State Technical University |
| record_format | Article |
| series | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| spelling | doaj.art-147477fb053e41b4b3e3e3e94af093062022-12-22T02:40:36ZengSamara State Technical UniversityVestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki1991-86152310-70812013-12-0117110614310.14498/vsgtu114031212On problem of nonexistence of dissipative estimate for discrete kinetic equationsEvgenii Vladimirovich Radkevich0Lomonosov Moscow State University, Faculty of Mechanics and MathematicsThe existence of a global solution to the discrete kinetic equations in Sobolev spaces is proved, its decomposition by summability is obtained, the influence of its oscillations generated by the interaction operator is explored. The existence of a submanifold ${\mathcal M}_{diss}$ of initial data $(u^0, v^0, w^0)$ for which the dissipative solution exists is proved. It’s shown that the interaction operator generates the solitons (progressive waves) as the nondissipative part of the solution when the initial data $(u^0, v^0, w^0)$ deviate from the submanifold ${\mathcal M}_{diss}$. The amplitude of solitons is proportional to the distance from $(u^0, v^0, w^0)$ to the submanifold ${\mathcal M}_{diss}$. It follows that the solution can stabilize as $t\to\infty$ only on compact sets of spatial variables.https://journals.eco-vector.com/1991-8615/article/viewFile/34699/23050dissipative estimatesdiscrete kinetic equations |
| spellingShingle | Evgenii Vladimirovich Radkevich On problem of nonexistence of dissipative estimate for discrete kinetic equations Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki dissipative estimates discrete kinetic equations |
| title | On problem of nonexistence of dissipative estimate for discrete kinetic equations |
| title_full | On problem of nonexistence of dissipative estimate for discrete kinetic equations |
| title_fullStr | On problem of nonexistence of dissipative estimate for discrete kinetic equations |
| title_full_unstemmed | On problem of nonexistence of dissipative estimate for discrete kinetic equations |
| title_short | On problem of nonexistence of dissipative estimate for discrete kinetic equations |
| title_sort | on problem of nonexistence of dissipative estimate for discrete kinetic equations |
| topic | dissipative estimates discrete kinetic equations |
| url | https://journals.eco-vector.com/1991-8615/article/viewFile/34699/23050 |
| work_keys_str_mv | AT evgeniivladimirovichradkevich onproblemofnonexistenceofdissipativeestimatefordiscretekineticequations |