Power geometry in nonlinear partial differential equations
Power Geometry (PG) is a new calculus developing the differential calculus and aimed at nonlinear problems. The main concept of PG is the study of nonlinear problems in logarithms of original coordinates. Then many relations nonlinear in the original coordinates become linear. The algorithms of PG a...
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| Опубліковано в: : | Український математичний вісник |
|---|---|
| Дата: | 2008 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2008
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/124295 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Power geometry in nonlinear partial differential equations / A.D. Bruno // Український математичний вісник. — 2008. — Т. 5, № 1. — С. 32-45. — Бібліогр.: 4 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862617182510252032 |
|---|---|
| author | Bruno, A.D. |
| author_facet | Bruno, A.D. |
| citation_txt | Power geometry in nonlinear partial differential equations / A.D. Bruno // Український математичний вісник. — 2008. — Т. 5, № 1. — С. 32-45. — Бібліогр.: 4 назв. — англ. |
| collection | DSpace DC |
| container_title | Український математичний вісник |
| description | Power Geometry (PG) is a new calculus developing the differential calculus and aimed at nonlinear problems. The main concept of PG is the study of nonlinear problems in logarithms of original coordinates. Then many relations nonlinear in the original coordinates become linear. The algorithms of PG are based on these linear relations. They allow to simplify equations, to resolve their singularities (including singular perturbations), to isolate their first approximations, and to find asymptotic forms and asymptotic expansions of their solutions. In particular, they give simple methods to identify the equations and systems as quasihomogeneous, and then to introduce for them self-similar coordinates. As an application, we consider the stationary spatial axially symmetric flow of the viscous compressible heat conducting gas around a semi-infinite needle. Other application: finding blow-up solutions.
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| first_indexed | 2025-12-07T13:10:59Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-124295 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1810-3200 |
| language | English |
| last_indexed | 2025-12-07T13:10:59Z |
| publishDate | 2008 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Bruno, A.D. 2017-09-23T16:47:37Z 2017-09-23T16:47:37Z 2008 Power geometry in nonlinear partial differential equations / A.D. Bruno // Український математичний вісник. — 2008. — Т. 5, № 1. — С. 32-45. — Бібліогр.: 4 назв. — англ. 1810-3200 2000 MSC. 200134, 200135 https://nasplib.isofts.kiev.ua/handle/123456789/124295 Power Geometry (PG) is a new calculus developing the differential calculus and aimed at nonlinear problems. The main concept of PG is the study of nonlinear problems in logarithms of original coordinates. Then many relations nonlinear in the original coordinates become linear. The algorithms of PG are based on these linear relations. They allow to simplify equations, to resolve their singularities (including singular perturbations), to isolate their first approximations, and to find asymptotic forms and asymptotic expansions of their solutions. In particular, they give simple methods to identify the equations and systems as quasihomogeneous, and then to introduce for them self-similar coordinates. As an application, we consider the stationary spatial axially symmetric flow of the viscous compressible heat conducting gas around a semi-infinite needle. Other application: finding blow-up solutions. The work was supported by RFBR, Grant 08-01-00082. en Інститут прикладної математики і механіки НАН України Український математичний вісник Power geometry in nonlinear partial differential equations Article published earlier |
| spellingShingle | Power geometry in nonlinear partial differential equations Bruno, A.D. |
| title | Power geometry in nonlinear partial differential equations |
| title_full | Power geometry in nonlinear partial differential equations |
| title_fullStr | Power geometry in nonlinear partial differential equations |
| title_full_unstemmed | Power geometry in nonlinear partial differential equations |
| title_short | Power geometry in nonlinear partial differential equations |
| title_sort | power geometry in nonlinear partial differential equations |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/124295 |
| work_keys_str_mv | AT brunoad powergeometryinnonlinearpartialdifferentialequations |