Uniqueness in a two-phase free-boundary problem

We investigate a two-phase free-boundary problem in heat propagation that in classical terms is formulated as follows: to find a continuous function u(x,t) defined in a domain D ⊂ ℝN×(0, T) which satisfies the equation. whenever u(x, t) ≠ 0, i.e., in the subdomains D+ = {(x,t)ε D : u(x,t)> 0}...

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Autores principales: Lederman, Claudia Beatriz, Wolanski, Noemi Irene
Publicado: 2001
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10799389_v6_n12_p1409_Lederman
http://hdl.handle.net/20.500.12110/paper_10799389_v6_n12_p1409_Lederman
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling paper:paper_10799389_v6_n12_p1409_Lederman2023-06-08T16:05:37Z Uniqueness in a two-phase free-boundary problem Lederman, Claudia Beatriz Wolanski, Noemi Irene We investigate a two-phase free-boundary problem in heat propagation that in classical terms is formulated as follows: to find a continuous function u(x,t) defined in a domain D ⊂ ℝN×(0, T) which satisfies the equation. whenever u(x, t) ≠ 0, i.e., in the subdomains D+ = {(x,t)ε D : u(x,t)> 0} and D- = {(x,t) < D : u(x,t) < 0}. Besides, we assume that both subdomains are separated by a smooth hypersurface, the free boundary, whose normal is never time-oriented and on which the following conditions are satisfied: Here M > 0 is a fixed constant, and the gradients are spatial sidederivatives in the usual two-phase sense. In addition, initial data are specified, as well as either Dirichlet or Neumann data on the parabolic boundary of D. The problem admits classical solutions only for good data and for small times. To overcome this problem several generalized concepts of solution have been proposed, among them the concepts of limit solution and viscosity solution. Continuing the work done for the one-phase problem we investigate conditions under which the three concepts agree and produce a unique solution for the two-phase problem. Fil:Lederman, C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Wolanski, N. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2001 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10799389_v6_n12_p1409_Lederman http://hdl.handle.net/20.500.12110/paper_10799389_v6_n12_p1409_Lederman
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description We investigate a two-phase free-boundary problem in heat propagation that in classical terms is formulated as follows: to find a continuous function u(x,t) defined in a domain D ⊂ ℝN×(0, T) which satisfies the equation. whenever u(x, t) ≠ 0, i.e., in the subdomains D+ = {(x,t)ε D : u(x,t)> 0} and D- = {(x,t) < D : u(x,t) < 0}. Besides, we assume that both subdomains are separated by a smooth hypersurface, the free boundary, whose normal is never time-oriented and on which the following conditions are satisfied: Here M > 0 is a fixed constant, and the gradients are spatial sidederivatives in the usual two-phase sense. In addition, initial data are specified, as well as either Dirichlet or Neumann data on the parabolic boundary of D. The problem admits classical solutions only for good data and for small times. To overcome this problem several generalized concepts of solution have been proposed, among them the concepts of limit solution and viscosity solution. Continuing the work done for the one-phase problem we investigate conditions under which the three concepts agree and produce a unique solution for the two-phase problem.
author Lederman, Claudia Beatriz
Wolanski, Noemi Irene
spellingShingle Lederman, Claudia Beatriz
Wolanski, Noemi Irene
Uniqueness in a two-phase free-boundary problem
author_facet Lederman, Claudia Beatriz
Wolanski, Noemi Irene
author_sort Lederman, Claudia Beatriz
title Uniqueness in a two-phase free-boundary problem
title_short Uniqueness in a two-phase free-boundary problem
title_full Uniqueness in a two-phase free-boundary problem
title_fullStr Uniqueness in a two-phase free-boundary problem
title_full_unstemmed Uniqueness in a two-phase free-boundary problem
title_sort uniqueness in a two-phase free-boundary problem
publishDate 2001
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10799389_v6_n12_p1409_Lederman
http://hdl.handle.net/20.500.12110/paper_10799389_v6_n12_p1409_Lederman
work_keys_str_mv AT ledermanclaudiabeatriz uniquenessinatwophasefreeboundaryproblem
AT wolanskinoemiirene uniquenessinatwophasefreeboundaryproblem
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