On kinetic formulation of first-order hyperbolic quasilinear systems
We give kinetic formulation of measure valued and strong measure valued solutions to the Cauchy problem for a first-order quasilinear equation. For the corresponding kinetic equation the class of existence and uniqueness to the Cauchy problem is extracted. This class consists of so-called entropy so...
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| Published in: | Український математичний вісник |
|---|---|
| Date: | 2004 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2004
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/124631 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On kinetic formulation of first-order hyperbolic quasilinear systems / E.Yu. Panov // Український математичний вісник. — 2004. — Т. 1, № 4. — С. 548-563. — Бібліогр.: 14 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862716097405386752 |
|---|---|
| author | Panov, E.Yu. |
| author_facet | Panov, E.Yu. |
| citation_txt | On kinetic formulation of first-order hyperbolic quasilinear systems / E.Yu. Panov // Український математичний вісник. — 2004. — Т. 1, № 4. — С. 548-563. — Бібліогр.: 14 назв. — англ. |
| collection | DSpace DC |
| container_title | Український математичний вісник |
| description | We give kinetic formulation of measure valued and strong measure valued solutions to the Cauchy problem for a first-order quasilinear equation. For the corresponding kinetic equation the class of existence and uniqueness to the Cauchy problem is extracted. This class consists of so-called entropy solutions, which correspond to strong measure valued solutions of the original problem. In the last section we generalized these results to the case of symmetric generally nonconservative multidimensional systems and introduce the notion of a strong measure valued solution, based only on the kinetic approach under consideration.
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| first_indexed | 2025-12-07T18:03:03Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-124631 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1810-3200 |
| language | English |
| last_indexed | 2025-12-07T18:03:03Z |
| publishDate | 2004 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Panov, E.Yu. 2017-09-30T12:40:46Z 2017-09-30T12:40:46Z 2004 On kinetic formulation of first-order hyperbolic quasilinear systems / E.Yu. Panov // Український математичний вісник. — 2004. — Т. 1, № 4. — С. 548-563. — Бібліогр.: 14 назв. — англ. 1810-3200 2000 MSC. 35L60, 35L45. https://nasplib.isofts.kiev.ua/handle/123456789/124631 We give kinetic formulation of measure valued and strong measure valued solutions to the Cauchy problem for a first-order quasilinear equation. For the corresponding kinetic equation the class of existence and uniqueness to the Cauchy problem is extracted. This class consists of so-called entropy solutions, which correspond to strong measure valued solutions of the original problem. In the last section we generalized these results to the case of symmetric generally nonconservative multidimensional systems and introduce the notion of a strong measure valued solution, based only on the kinetic approach under consideration. en Інститут прикладної математики і механіки НАН України Український математичний вісник On kinetic formulation of first-order hyperbolic quasilinear systems Article published earlier |
| spellingShingle | On kinetic formulation of first-order hyperbolic quasilinear systems Panov, E.Yu. |
| title | On kinetic formulation of first-order hyperbolic quasilinear systems |
| title_full | On kinetic formulation of first-order hyperbolic quasilinear systems |
| title_fullStr | On kinetic formulation of first-order hyperbolic quasilinear systems |
| title_full_unstemmed | On kinetic formulation of first-order hyperbolic quasilinear systems |
| title_short | On kinetic formulation of first-order hyperbolic quasilinear systems |
| title_sort | on kinetic formulation of first-order hyperbolic quasilinear systems |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/124631 |
| work_keys_str_mv | AT panoveyu onkineticformulationoffirstorderhyperbolicquasilinearsystems |