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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| Опубліковано в: : | Український математичний вісник |
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| Дата: | 2004 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2004
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/124631 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | 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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| ISSN: | 1810-3200 |