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Open Access Green as soon as Postprint is submitted to ZB.
Stability of non-isolated asymptotic profiles for fast diffusion.
Commun. Math. Phys. 345, 77-100 (2016)
The stability of asymptotic profiles of solutions to the Cauchy–Dirichlet problem for fast diffusion equation (FDE, for short) is discussed. The main result of the present paper is the stability of any asymptotic profiles of least energy. It is noteworthy that this result can cover non-isolated profiles, e.g., those for thin annular domain cases. The method of proof is based on the Łojasiewicz–Simon inequality, which is usually used to prove the convergence of solutions to prescribed limits, as well as a uniform extinction estimate for solutions to FDE. Besides, local minimizers of an energy functional associated with this issue are characterized. Furthermore, the instability of positive radial asymptotic profiles in thin annular domains is also proved by applying the Łojasiewicz–Simon inequality in a different way.
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Publication type
Article: Journal article
Document type
Scientific Article
Keywords
Semilinear Elliptic-equations; Singular Parabolic Equations; Simon Gradient Inequality; Evolution-equations; Positive Solutions; Decay; Convergence; Equilibrium; Extinction; Existence
ISSN (print) / ISBN
0010-3616
e-ISSN
1432-0916
Quellenangaben
Volume: 345,
Issue: 1,
Pages: 77-100
Publisher
Springer
Publishing Place
New York
Reviewing status
Peer reviewed
Institute(s)
Institute of Computational Biology (ICB)