Existence of global solutions with slow decay and unbounded free boundary for a superlinear Stefan problem. (English) Zbl 1006.35103

Fila, Marek; Souplet, Philippe

Interfaces Free Bound. 3, No. 3, 337-344 (2001).

This article studies global solutions to one-dimensional Stefan problems of the superlinear heat equation, and is closely related to a paper by H. Ghidouche, Ph. Souplet and D. Tarzia [Proc. Am. Math. Soc. 129, 781-792 (2001; Zbl 0959.35087)]. The authors provide a correction to an error in the proof of solution decay in the previous paper, and also derive a priori \(L^\infty\)-norm estimates for global solutions, and in terms of the estimates prove that there exist global solutions with slow decay and unbounded free boundary.

Reviewer: Ning Su (Beijing)

MSC:

35R35	Free boundary problems for PDEs
35K55	Nonlinear parabolic equations
35B40	Asymptotic behavior of solutions to PDEs

Keywords:

global solutions; one-dimensional Stefan problems; superlinear heat equation; a priori \(L^\infty\)-norm estimates; unbounded free boundary

Citations:

Zbl 0959.35087