Semilinear equations in a plane and quasiconformal mappings
We consider generalizations of the Bieberbach equation with nonlinear right parts, which makes it possible to study many problems of mathematical physics in inhomogeneous and anisotropic media with smooth characteristics. We establish interconnections of these semilinear equations with quasiconfor...
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| Date: | 2017 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Видавничий дім "Академперіодика" НАН України
2017
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| Series: | Доповіді НАН України |
| Subjects: | |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/126329 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Semilinear equations in a plane and quasiconformal mappings / V.Ya. Gutlyanskiĭ, O.V. Nesmelova, V.I. Ryazanov // Доповіді Національної академії наук України. — 2017. — № 1. — С. 10-16. — Бібліогр.: 15 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | We consider generalizations of the Bieberbach equation with nonlinear right parts, which makes it possible to study
many problems of mathematical physics in inhomogeneous and anisotropic media with smooth characteristics. We
establish interconnections of these semilinear equations with quasiconformal mappings, obtain on this basis, a series
of theorems on the existence of their solutions that blow-up on the boundary of a unit disk, as well as on punctured
unit disks and rings, and give their explicit representations. |
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