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

Daniele Andreucci; Marianne K. Korten

Revista Matemática Iberoamericana (1993)

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

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topAndreucci, 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 > 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 < t < 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 > 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 < t < 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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