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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todo:paper_10799389_v6_n12_p1409_Lederman2023-10-03T16:03:42Z Uniqueness in a two-phase free-boundary problem Lederman, C. Wolanski, N. Vázquez, J.L. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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. |
| format |
JOUR |
| author |
Lederman, C. Wolanski, N. Vázquez, J.L. |
| spellingShingle |
Lederman, C. Wolanski, N. Vázquez, J.L. Uniqueness in a two-phase free-boundary problem |
| author_facet |
Lederman, C. Wolanski, N. Vázquez, J.L. |
| author_sort |
Lederman, C. |
| 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 |
| url |
http://hdl.handle.net/20.500.12110/paper_10799389_v6_n12_p1409_Lederman |
| work_keys_str_mv |
AT ledermanc uniquenessinatwophasefreeboundaryproblem AT wolanskin uniquenessinatwophasefreeboundaryproblem AT vazquezjl uniquenessinatwophasefreeboundaryproblem |
| _version_ |
1807315216801726464 |