Bubbling and extinction for some fast diffusion equations in bounded domains

Jin, Tianling; Xiong, Jingang

doi:10.1090/btran/165

Bubbling and extinction for some fast diffusion equations in bounded domains
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by Tianling Jin and Jingang Xiong

Trans. Amer. Math. Soc. Ser. B 10 (2023), 1287-1332

DOI: https://doi.org/10.1090/btran/165

Published electronically: September 15, 2023

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Abstract:

We study a Sobolev critical fast diffusion equation in bounded domains with the Brézis-Nirenberg effect. We obtain extinction profiles of its positive solutions, and show that the convergence rates of the relative error in regular norms are at least polynomial. Exponential decay rates are proved for generic domains. Our proof makes use of its regularity estimates, a curvature type evolution equation, as well as blow up analysis. Results for Sobolev subcritical fast diffusion equations are also obtained.

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