Geodesic
Existence of global solutions with slow decay and unbounded free boundary for a superlinear Stefan problem
Marek Fila1 ; Philippe Souplet2
1Comenius University, Bratislava, Slovak Republic
2Université de Paris XIII, Villetaneuse, France
Interfaces and free boundaries, Tome 3 (2001) no. 3, pp. 337-344

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DOI

We consider a one-phase Stefan problem for the heat equation with a superlinear reaction term. It is known from a previous work (Ghidouche, Souplet, & Tarzia [5]) that all global solutions are bounded and decay uniformly to 0. Moreover, it was shown in Ghidouche, Souplet, & Tarzia [5] that either: (i) the free boundary converges to a finite limit and the solution decays at an exponential rate, or (ii) the free boundary grows up to infinity and the decay rate is at most polynomial, and it was also proved that small data solutions behave like (i).
DOI : 10.4171/ifb/43
Classification : 46-XX, 60-XX
Mots-clés : Nonlinear reaction-diffusion equation, free boundary condition, Stefan problem, global existence, decay, a priori estimates

Marek Fila  1   ; Philippe Souplet  2

1 Comenius University, Bratislava, Slovak Republic
2 Université de Paris XIII, Villetaneuse, France 
Marek Fila; Philippe Souplet. Existence of global solutions with slow decay and unbounded free boundary for a superlinear Stefan problem. Interfaces and free boundaries, Tome 3 (2001) no. 3, pp. 337-344. doi: 10.4171/ifb/43
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     title = {Existence of global solutions with slow decay and unbounded free boundary for a superlinear {Stefan} problem},
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     year = {2001},
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     doi = {10.4171/ifb/43},
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