Asymptotic convergence of the Stefan problem to Hele-Shaw
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- by Fernando Quirós and Juan Luis Vázquez PDF
- Trans. Amer. Math. Soc. 353 (2001), 609-634 Request permission
Abstract:
We discuss the asymptotic behaviour of weak solutions to the Hele-Shaw and one-phase Stefan problems in exterior domains. We prove that, if the space dimension is greater than one, the asymptotic behaviour is given in both cases by the solution of the Dirichlet exterior problem for the Laplacian in the interior of the positivity set and by a singular, radial and self-similar solution of the Hele-Shaw flow near the free boundary. We also show that the free boundary approaches a sphere as $t\to \infty$, and give the precise asymptotic growth rate for the radius.References
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Additional Information
- Fernando Quirós
- Affiliation: Departamento de Matemáticas, Universidad Autónoma, 28049 Madrid, Spain
- Juan Luis Vázquez
- Affiliation: Departamento de Matemáticas, Universidad Autónoma, 28049 Madrid, Spain
- Received by editor(s): December 31, 1996
- Received by editor(s) in revised form: October 28, 1997
- Published electronically: October 23, 2000
- © Copyright 2000 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 353 (2001), 609-634
- MSC (2000): Primary 35B40, 35R35
- DOI: https://doi.org/10.1090/S0002-9947-00-02739-2
- MathSciNet review: 1804510