# Initial traces of solutions to a one-phase Stefan problem in an infinite strip.

• Volume: 9, Issue: 2, page 315-332
• ISSN: 0213-2230

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## Abstract

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The main result of this paper is an integral estimate valid for non-negative solutions (with no reference to initial data) u ∈ L1loc (Rn x (0,T)) to(0.1)   ut - Δ(u - 1)+ = 0,  in D'(Rn x (0,T)),for T &gt; 0, n ≥ 1. Equation (0.1) is a formulation of a one-phase Stefan problem: in this connection u is the enthalpy, (u - 1)+ the temperature, and u = 1 the critical temperature of change of phase. Our estimate may be written in the form(0.2)  ∫Rn u(x,t) e-|x|2 / (2 (T - t)) dx ≤ C,   0 &lt; t &lt; T,where C depends on n, T, t, u but it stays bounded as T → 0.

## How to cite

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Andreucci, Daniele, and Korten, Marianne K.. "Initial traces of solutions to a one-phase Stefan problem in an infinite strip.." Revista Matemática Iberoamericana 9.2 (1993): 315-332. <http://eudml.org/doc/39441>.

@article{Andreucci1993,
abstract = {The main result of this paper is an integral estimate valid for non-negative solutions (with no reference to initial data) u ∈ L1loc (Rn x (0,T)) to(0.1)   ut - Δ(u - 1)+ = 0,  in D'(Rn x (0,T)),for T &gt; 0, n ≥ 1. Equation (0.1) is a formulation of a one-phase Stefan problem: in this connection u is the enthalpy, (u - 1)+ the temperature, and u = 1 the critical temperature of change of phase. Our estimate may be written in the form(0.2)  ∫Rn u(x,t) e-|x|2 / (2 (T - t)) dx ≤ C,   0 &lt; t &lt; T,where C depends on n, T, t, u but it stays bounded as T → 0.},
author = {Andreucci, Daniele, Korten, Marianne K.},
journal = {Revista Matemática Iberoamericana},
keywords = {Trazas; Cambio de fase; Medida de Radón; Problema de Cauchy; Regularidad; regularity; a priori estimate; existence and uniqueness of an initial trace; existence of a unique solution to the Cauchy problem},
language = {eng},
number = {2},
pages = {315-332},
title = {Initial traces of solutions to a one-phase Stefan problem in an infinite strip.},
url = {http://eudml.org/doc/39441},
volume = {9},
year = {1993},
}

TY - JOUR
AU - Andreucci, Daniele
AU - Korten, Marianne K.
TI - Initial traces of solutions to a one-phase Stefan problem in an infinite strip.
JO - Revista Matemática Iberoamericana
PY - 1993
VL - 9
IS - 2
SP - 315
EP - 332
AB - The main result of this paper is an integral estimate valid for non-negative solutions (with no reference to initial data) u ∈ L1loc (Rn x (0,T)) to(0.1)   ut - Δ(u - 1)+ = 0,  in D'(Rn x (0,T)),for T &gt; 0, n ≥ 1. Equation (0.1) is a formulation of a one-phase Stefan problem: in this connection u is the enthalpy, (u - 1)+ the temperature, and u = 1 the critical temperature of change of phase. Our estimate may be written in the form(0.2)  ∫Rn u(x,t) e-|x|2 / (2 (T - t)) dx ≤ C,   0 &lt; t &lt; T,where C depends on n, T, t, u but it stays bounded as T → 0.
LA - eng
KW - Trazas; Cambio de fase; Medida de Radón; Problema de Cauchy; Regularidad; regularity; a priori estimate; existence and uniqueness of an initial trace; existence of a unique solution to the Cauchy problem
UR - http://eudml.org/doc/39441
ER -

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