On the domain dependence of solutions to the two-phase Stefan problem

Eduard Feireisl; Hana Petzeltová

Applications of Mathematics (2000)

  • Volume: 45, Issue: 2, page 131-144
  • ISSN: 0862-7940

Abstract

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We prove that solutions to the two-phase Stefan problem defined on a sequence of spatial domains Ω n ⊂ ℝ N converge to a solution of the same problem on a domain Ω where Ω is the limit of Ω n in the sense of Mosco. The corresponding free boundaries converge in the sense of Lebesgue measure on ℝ N .

How to cite

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Feireisl, Eduard, and Petzeltová, Hana. "On the domain dependence of solutions to the two-phase Stefan problem." Applications of Mathematics 45.2 (2000): 131-144. <http://eudml.org/doc/33052>.

@article{Feireisl2000,
abstract = {We prove that solutions to the two-phase Stefan problem defined on a sequence of spatial domains $\Omega _n\subset \mathbb \{R\}^N$ converge to a solution of the same problem on a domain $\Omega $ where $\Omega $ is the limit of $\Omega _n $ in the sense of Mosco. The corresponding free boundaries converge in the sense of Lebesgue measure on $\mathbb \{R\}^N$.},
author = {Feireisl, Eduard, Petzeltová, Hana},
journal = {Applications of Mathematics},
keywords = {Stefan problem; domain dependence; Mosco-type covergence of domains; Stefan problem; domain dependence; Mosco-type covergence of domains},
language = {eng},
number = {2},
pages = {131-144},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the domain dependence of solutions to the two-phase Stefan problem},
url = {http://eudml.org/doc/33052},
volume = {45},
year = {2000},
}

TY - JOUR
AU - Feireisl, Eduard
AU - Petzeltová, Hana
TI - On the domain dependence of solutions to the two-phase Stefan problem
JO - Applications of Mathematics
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 45
IS - 2
SP - 131
EP - 144
AB - We prove that solutions to the two-phase Stefan problem defined on a sequence of spatial domains $\Omega _n\subset \mathbb {R}^N$ converge to a solution of the same problem on a domain $\Omega $ where $\Omega $ is the limit of $\Omega _n $ in the sense of Mosco. The corresponding free boundaries converge in the sense of Lebesgue measure on $\mathbb {R}^N$.
LA - eng
KW - Stefan problem; domain dependence; Mosco-type covergence of domains; Stefan problem; domain dependence; Mosco-type covergence of domains
UR - http://eudml.org/doc/33052
ER -

References

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