Artículo
Lederman, C.; Wolanski, N.; Vázquez, J.L. "Uniqueness in a two-phase free-boundary problem" (2001) Advances in Differential Equations. 6(12):1409-1442
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Abstract:
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.
Registro:
| Documento: | Artículo |
| Título: | Uniqueness in a two-phase free-boundary problem |
| Autor: | Lederman, C.; Wolanski, N.; Vázquez, J.L. |
| Filiación: | Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, (1428) Buenos Aires, Argentina Departamento de Matemática, Universidad Autónoma de Madrid, Madrid, Spain |
| Año: | 2001 |
| Volumen: | 6 |
| Número: | 12 |
| Página de inicio: | 1409 |
| Página de fin: | 1442 |
| Título revista: | Advances in Differential Equations |
| Título revista abreviado: | Adv. Differ. Equ. |
| ISSN: | 10799389 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10799389_v6_n12_p1409_Lederman |
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Citas:
---------- APA ----------
Lederman, C., Wolanski, N. & Vázquez, J.L. (2001) . Uniqueness in a two-phase free-boundary problem. Advances in Differential Equations, 6(12), 1409-1442.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10799389_v6_n12_p1409_Lederman [ ]
---------- CHICAGO ----------
Lederman, C., Wolanski, N., Vázquez, J.L. "Uniqueness in a two-phase free-boundary problem" . Advances in Differential Equations 6, no. 12 (2001) : 1409-1442.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10799389_v6_n12_p1409_Lederman [ ]
---------- MLA ----------
Lederman, C., Wolanski, N., Vázquez, J.L. "Uniqueness in a two-phase free-boundary problem" . Advances in Differential Equations, vol. 6, no. 12, 2001, pp. 1409-1442.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10799389_v6_n12_p1409_Lederman [ ]
---------- VANCOUVER ----------
Lederman, C., Wolanski, N., Vázquez, J.L. Uniqueness in a two-phase free-boundary problem. Adv. Differ. Equ. 2001;6(12):1409-1442.Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10799389_v6_n12_p1409_Lederman [ ]
