JournalsaihpcVol. 31, No. 6pp. 1155–1173

Symmetry and stability of asymptotic profiles for fast diffusion equations in annuli

  • Goro Akagi

    Graduate School of System Informatics, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe 657-8501, Japan

  • Ryuji Kajikiya

    Department of Mathematics, Faculty of Science and Engineering, Saga University, Saga 840-8502, Japan
Symmetry and stability of asymptotic profiles for fast diffusion equations in annuli cover
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Abstract

This paper is concerned with stability analysis of asymptotic profiles for (possibly sign-changing) solutions vanishing in finite time of the Cauchy–Dirichlet problems for fast diffusion equations in annuli. It is proved that the unique positive radial profile is not asymptotically stable, and moreover, it is unstable for the two-dimensional annulus. Furthermore, the method of stability analysis presented here will be also applied to exhibit symmetry breaking of least energy solutions.

Cite this article

Goro Akagi, Ryuji Kajikiya, Symmetry and stability of asymptotic profiles for fast diffusion equations in annuli. Ann. Inst. H. Poincaré Anal. Non Linéaire 31 (2014), no. 6, pp. 1155–1173

DOI 10.1016/J.ANIHPC.2013.08.006