Stability of Non-Isolated Asymptotic Profiles for Fast Diffusion

研究成果: Article査読

3 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)77-100
ページ数24
ジャーナルCommunications in Mathematical Physics
345
1
DOI
出版ステータスPublished - 2016 7月 1

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 数理物理学

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