Proper spaces for the asymptotic convergence of solutions of porous medium equation

Proper spaces for the asymptotic convergence of solutions of porous medium equation

In this paper, we consider the problem that a weighted L∞ space Wϑ(RN) is proper or not for the asymptotic convergence of solutions of the porous medium equation. We find that there exists a critical exponent ϑ=σ of the proper spaces for the asymptotic problem proposed by Alikakos and Rostamian (198...

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Veröffentlicht in:Nonlinear analysis: real world applications 2017-12, Vol.38, p.261-270
Hauptverfasser: Wang, Liangwei, Yin, Jingxue
Format: Artikel
Sprache:eng
Schlagworte:
Asymptotic convergence
Asymptotic methods
Asymptotic properties
Cauchy problems
Convergence
Improper spaces
Partial differential equations
Porous media
Porous medium equation
Proper spaces
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Zusammenfassung:In this paper, we consider the problem that a weighted L∞ space Wϑ(RN) is proper or not for the asymptotic convergence of solutions of the porous medium equation. We find that there exists a critical exponent ϑ=σ of the proper spaces for the asymptotic problem proposed by Alikakos and Rostamian (1984).
ISSN:1468-1218
1878-5719
DOI:10.1016/j.nonrwa.2017.05.004