Near-field asymptotics for the porous medium equation in exterior domains. The critical two-dimensional case
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...
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2018
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00361410_v50_n3_p2664_Cortazar http://hdl.handle.net/20.500.12110/paper_00361410_v50_n3_p2664_Cortazar |
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paper:paper_00361410_v50_n3_p2664_Cortazar2023-06-08T15:01:56Z Near-field asymptotics for the porous medium equation in exterior domains. The critical two-dimensional case 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 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. 2018 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00361410_v50_n3_p2664_Cortazar http://hdl.handle.net/20.500.12110/paper_00361410_v50_n3_p2664_Cortazar |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
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 |
| spellingShingle |
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 Near-field asymptotics for the porous medium equation in exterior domains. The critical two-dimensional case |
| topic_facet |
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 |
| description |
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. |
| title |
Near-field asymptotics for the porous medium equation in exterior domains. The critical two-dimensional case |
| title_short |
Near-field asymptotics for the porous medium equation in exterior domains. The critical two-dimensional case |
| title_full |
Near-field asymptotics for the porous medium equation in exterior domains. The critical two-dimensional case |
| title_fullStr |
Near-field asymptotics for the porous medium equation in exterior domains. The critical two-dimensional case |
| title_full_unstemmed |
Near-field asymptotics for the porous medium equation in exterior domains. The critical two-dimensional case |
| title_sort |
near-field asymptotics for the porous medium equation in exterior domains. the critical two-dimensional case |
| publishDate |
2018 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00361410_v50_n3_p2664_Cortazar http://hdl.handle.net/20.500.12110/paper_00361410_v50_n3_p2664_Cortazar |
| _version_ |
1768543886695727104 |