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May  2008, 7(3): 591-600. doi: 10.3934/cpaa.2008.7.591

Regularity for solutions of the two-phase Stefan problem

Marianne Korten 1, and  Charles N. Moore 1,

1. 

Department of Mathematics, Kansas State University, Manhattan, KS 66506, United States

Received  March 2007 Revised  October 2007 Published  February 2008

We consider the two-phase Stefan problem $u_t=\Delta\alpha(u)$ where $\alpha(u) =u+1$ for $u<-1$, $\alpha(u) =0$ for $-1 \leq u \leq 1$, and $\alpha(u)=u-1$ for $u \geq 1$. We show that if $u$ is an $L_{l o c}^2$ distributional solution then $\alpha(u)$ has $L_{l o c}^2$ derivatives in time and space. We also show $|\alpha(u)|$ is subcaloric and conclude that $\alpha(u)$ is continuous.
Keywords: Stefan problem, degenerate parabolic equation..
Mathematics Subject Classification: Primary: 35K65; Secondary: 80A2.
Citation: Marianne Korten, Charles N. Moore. Regularity for solutions of the two-phase Stefan problem. Communications on Pure and Applied Analysis, 2008, 7 (3) : 591-600. doi: 10.3934/cpaa.2008.7.591
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