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Статья «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"»

Авторы:
  • Архипова А.А.1
стр. 118-151
Платно
1 Московский государственный университет имени М.В. Ломоносова, химический факультет 119992 Москва, Ленинские горы, 1, стр. 3
  • SDI: 007.001.0234-0852.2019.031.002.5
Ключевые слова:
  • parabolic systems
  • strong nonlinearity
  • global solvability
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” crossing this curve. The two-phase conditions are given on this curve and the CauchyADirihlet conditions hold at the parabolic boundary of the main parabolic cylinder. The existence of a weak Etelder 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.

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