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The bidimensional Stefan problem with convection: The time dependent case. (English) Zbl 0547.35117
This paper considers the time dependent Stefan problem with convection in the fluid phase governed by the Stokes equation, and with adherence of the fluid on the lateral boundaries. Let $$\Omega$$ be a bounded daomain in $$R^ 2$$ with smooth boundary. The two phase Stefan problem is studied on the region $$\Omega \times (0,T)$$, $$T>0$$. The existence of a weak solution is obtained via the introduction of a temperature dependent penalty term in the fluid flow equation, together with the application of various compactness arguments.
Reviewer: M.Ullrich

##### MSC:
 35R35 Free boundary problems for PDEs 35A05 General existence and uniqueness theorems (PDE) (MSC2000) 35Q30 Navier-Stokes equations
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