Limit of kinetic term for a Stefan problem

Pages: 741 - 750, Issue Special, September 2007

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Piotr B. Mucha - Warsaw University, Inst. of Applied Math. and Mech., ul. Banacha 2, 02-097 Warszawa, Poland (email)

Abstract: We investigate solutions to the one-phase quasi-stationary Stefan problem with the surface tension and kinetic term. Main results show existence of unique regular solutions with a suitable bound which enables to obtain the limit as the kinetic term is vanishing. Our problem is considered in anisotropic Besov spaces locally in time.

Keywords:  Stefan problems, curvature, Besov spaces, vanishing kinetic effects, nonlocal parabolic systems, optimal regularity.
Mathematics Subject Classification:  Primary: 35R35, 35K55.

Received: September 2006;      Revised: April 2007;      Published: September 2007.