On the structure of characteristic surfaces related with partial differential equations of first and higher orders. Pt 2
The generalized characteristics method is developed in the framework of the geometric Monge picture. The Hopf – Lax-type extremality solutions to a wide class of Cauchy problem for nonlinear partial differential equations of first and higher orders are derived. The special Hamilton – Jacobi-type ca...
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| Дата: | 2005 |
|---|---|
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2005
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| Назва видання: | Нелінійні коливання |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/178021 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | On the structure of characteristic surfaces related with partial differential equations of first and higher orders. Pt 2 / N.K. Prykarpatska // Нелінійні коливання. — 2005. — Т. 8, № 4. — С. 529-543. — Бібліогр.: 20 назв. — англ. |
Репозитарії
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irk-123456789-178021 |
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irk-123456789-1780212021-02-18T01:27:43Z On the structure of characteristic surfaces related with partial differential equations of first and higher orders. Pt 2 Prykarpatska, N.K. The generalized characteristics method is developed in the framework of the geometric Monge picture. The Hopf – Lax-type extremality solutions to a wide class of Cauchy problem for nonlinear partial differential equations of first and higher orders are derived. The special Hamilton – Jacobi-type case is analized separately. The exact extremality Hopf – Lax-type solution for Cauchy problem to the nonlinear Burgers equation is received, its linearization to the Hopf – Cole expression and to the related Airy-type linear partial differential equation is found and discussed. Розвинуто узагальнений метод характеристик у рамках геометричного пiдходу Монжа. Отримано екстремальнi розв’язки типу Хопфа – Лакса широкого класу задач Кошi для нелiнiйних диференцiальних рiвнянь з частинними похiдними першого та вищих порядкiв. Окремо дослiджено спецiальний випадок типу Гамiльтона – Якобi. Отримано точний екстремальний розв’язок типу Хопфа – Лакса задачi Кошi для нелiнiйного рiвняння Бюргерса. Знайдено та проаналiзовано його лiнеаризацiю у виглядi виразу Хопфа – Коула та пов’язаного з ним лiнiйного диференцiального рiвняння з частинними похiдними типу Ейрi. 2005 Article On the structure of characteristic surfaces related with partial differential equations of first and higher orders. Pt 2 / N.K. Prykarpatska // Нелінійні коливання. — 2005. — Т. 8, № 4. — С. 529-543. — Бібліогр.: 20 назв. — англ. 1562-3076 http://dspace.nbuv.gov.ua/handle/123456789/178021 517.9 en Нелінійні коливання Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
The generalized characteristics method is developed in the framework of the geometric Monge picture. The
Hopf – Lax-type extremality solutions to a wide class of Cauchy problem for nonlinear partial differential equations of first and higher orders are derived. The special Hamilton – Jacobi-type case is analized
separately. The exact extremality Hopf – Lax-type solution for Cauchy problem to the nonlinear Burgers
equation is received, its linearization to the Hopf – Cole expression and to the related Airy-type linear
partial differential equation is found and discussed. |
| format |
Article |
| author |
Prykarpatska, N.K. |
| spellingShingle |
Prykarpatska, N.K. On the structure of characteristic surfaces related with partial differential equations of first and higher orders. Pt 2 Нелінійні коливання |
| author_facet |
Prykarpatska, N.K. |
| author_sort |
Prykarpatska, N.K. |
| title |
On the structure of characteristic surfaces related with partial differential equations of first and higher orders. Pt 2 |
| title_short |
On the structure of characteristic surfaces related with partial differential equations of first and higher orders. Pt 2 |
| title_full |
On the structure of characteristic surfaces related with partial differential equations of first and higher orders. Pt 2 |
| title_fullStr |
On the structure of characteristic surfaces related with partial differential equations of first and higher orders. Pt 2 |
| title_full_unstemmed |
On the structure of characteristic surfaces related with partial differential equations of first and higher orders. Pt 2 |
| title_sort |
on the structure of characteristic surfaces related with partial differential equations of first and higher orders. pt 2 |
| publisher |
Інститут математики НАН України |
| publishDate |
2005 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/178021 |
| citation_txt |
On the structure of characteristic surfaces related with partial differential equations of first and higher orders. Pt 2 / N.K. Prykarpatska // Нелінійні коливання. — 2005. — Т. 8, № 4. — С. 529-543. — Бібліогр.: 20 назв. — англ. |
| series |
Нелінійні коливання |
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2023-10-18T22:45:01Z |
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2023-10-18T22:45:01Z |
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1796156334739030016 |