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.
|Translated title of the contribution||Cлабая глобальная разрешимость двухфазной проблемы для класса параболических систем с сильной нелинейностью по градиенту. Случай двух пространственных переменных.|
|Journal||St. Petersburg Mathematical Journal|
|Publication status||Published - 2020|
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