| 概要 |
In this talk, we discuss the optimal rate of convergence to asymptotic
profiles of solutions, which vanish in finite time, to the Fast
Diffusion Equation posed on bounded domains. Quantitative studies in
this direction have developed significantly since the celebrated work
of Bonforte and Figalli (2021). However, in most existing results,
asymptotic profiles are assumed to be nondegenerate, meaning that the
linearized operator has a trivial kernel. In fact, such nondegeneracy
holds for generic domains. On the other hand, it is well known that
least-energy solutions to the Emden-Fowler equation in thin annuli are
nonradial. As a consequence, they are degenerate and thus fall outside
the scope of previous works. In this talk, inspired by recent work of
König and Yu (2024+), we establish the optimal convergence rate to
such degenerate asymptotic profiles for certain space dimensions. This
talk is based on a recent joint work with Norihisa Ikoma (Keio
University) and Yasunori Maekawa (Kyoto University).
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