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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| Date: | 2005 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2005
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| Series: | Нелінійні коливання |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/178021 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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. |
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