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Алгебра и анализ, 2019, том 31, выпуск 2, страницы 118–151
(Mi aa1640)
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Эта публикация цитируется в 3 научных статьях (всего в 3 статьях)
Статьи
Weak global solvability of the two-phase problem for a class of parabolic systems with strong nonlinearity in the gradient. The case of two spatial variables
A. A. Arkhipova St. Petersburg State University, Universitetskaya nab. 7/9, 199034, St-Petersburg, Russia
Аннотация:
A class of quasilinear parabolic systems with nondiagonal principal matrix and strongly nonlinear additional terms is considered. The elliptic operator of the system has a variational structure and is generated by a quadratic functional with a nondiagonal matrix. A plane domain of the spatial variables is divided by a smooth curve in two subdomains and the principal matrix of the system has a “jump” when crossing this curve. The two-phase conditions are given on this curve and the Cauchy-Dirichlet conditions hold at the parabolic boundary of the main parabolic cylinder. The existence of a weak Hölder continuous global solution of the two-phase problem is proved. The problem can be regarded as a construction of the heat flow from a given vector-function to an extremal of the functional.
Ключевые слова:
parabolic systems, strong nonlinearity, global solvability.
Поступила в редакцию: 30.11.2018
Образец цитирования:
A. A. Arkhipova, “Weak global solvability of the two-phase problem for a class of parabolic systems with strong nonlinearity in the gradient. The case of two spatial variables”, Алгебра и анализ, 31:2 (2019), 118–151; St. Petersburg Math. J., 31:2 (2019), 273–296
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/aa1640 https://www.mathnet.ru/rus/aa/v31/i2/p118
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Страница аннотации: | 271 | PDF полного текста: | 40 | Список литературы: | 62 | Первая страница: | 16 |
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