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Abstract:

We consider the porous medium equation in an exterior two-dimensional domain that excludes a hole, with zero Dirichlet data on its boundary. Gilding and Goncerzewicz proved in 2007 that in the far-field scale, which is the adequate one to describe the movement of the free boundary, solutions to this problem with integrable and compactly supported initial data behave as an instantaneous point-source solution for the equation with a variable mass that decays to 0 in a precise way, determined by the initial data and the hole. In this paper, starting from their result in the far field, we study the large time behavior in the near field, in scales that evolve more slowly than the free boundary. In this way we get, in particular, the final profile and decay rate on compact sets. Spatial dimension two is critical for this problem, and involves logarithmic corrections. © 2018 Society for Industrial and Applied Mathematics.

Registro:

Documento: Artículo
Título:Near-field asymptotics for the porous medium equation in exterior domains. The critical two-dimensional case
Autor:Cortázar, C.; Quirós, F.; Wolanski, N.
Filiación:Departamento de Matemática, Pontificia Universidad Católica de Chile, Santiago, Chile
Departamento de Matemáticas, Universidad Autónoma de Madrid, Madrid, 28049, Spain
Departamento de Matemática, FCEyN, Universidad de Buenos Aires, IMAS, CONICET, Buenos Aires, 1428, Argentina
Palabras clave:Asymptotic behavior; Exterior domain; Matched asymptotics; Porous medium equation; Decay (organic); Plating; Asymptotic behaviors; Compactly supported; Exterior domain; Instantaneous point source; Logarithmic corrections; Matched asymptotics; Porous medium equation; Two-dimensional domain; Porous materials
Año:2018
Volumen:50
Número:3
Página de inicio:2664
Página de fin:2680
DOI: http://dx.doi.org/10.1137/16M110191X
Título revista:SIAM Journal on Mathematical Analysis
Título revista abreviado:SIAM J. Math. Anal.
ISSN:00361410
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00361410_v50_n3_p2664_Cortazar

Referencias:

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Citas:

---------- APA ----------
Cortázar, C., Quirós, F. & Wolanski, N. (2018) . Near-field asymptotics for the porous medium equation in exterior domains. The critical two-dimensional case. SIAM Journal on Mathematical Analysis, 50(3), 2664-2680.
http://dx.doi.org/10.1137/16M110191X
---------- CHICAGO ----------
Cortázar, C., Quirós, F., Wolanski, N. "Near-field asymptotics for the porous medium equation in exterior domains. The critical two-dimensional case" . SIAM Journal on Mathematical Analysis 50, no. 3 (2018) : 2664-2680.
http://dx.doi.org/10.1137/16M110191X
---------- MLA ----------
Cortázar, C., Quirós, F., Wolanski, N. "Near-field asymptotics for the porous medium equation in exterior domains. The critical two-dimensional case" . SIAM Journal on Mathematical Analysis, vol. 50, no. 3, 2018, pp. 2664-2680.
http://dx.doi.org/10.1137/16M110191X
---------- VANCOUVER ----------
Cortázar, C., Quirós, F., Wolanski, N. Near-field asymptotics for the porous medium equation in exterior domains. The critical two-dimensional case. SIAM J. Math. Anal. 2018;50(3):2664-2680.
http://dx.doi.org/10.1137/16M110191X