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

Akagi, Goro; Kajikiya, Ryuji

Annales de l'I.H.P. Analyse non linéaire, Tome 31 (2014) no. 6, pp. 1155-1173.

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.

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