Collapsing-ring blowup solutions for the nonlinear heat equation

In this paper, we construct a singular standing ring solution of the nonlinear heat in the radial case. We give rigorous proof for the existence of a ring blow-up solution in finite time. This result was predicted formally by Baruch, Fibich and Gavish \cite{BFGpd10}. We also prove the stability of t...

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Bibliographic Details
Main Authors Duan, Senhao, Nouaili, Nejla, Zaag, Hatem
Format Journal Article
LanguageEnglish
Published 06.06.2024
Subjects
Mathematics - Analysis of PDEs
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Summary:In this paper, we construct a singular standing ring solution of the nonlinear heat in the radial case. We give rigorous proof for the existence of a ring blow-up solution in finite time. This result was predicted formally by Baruch, Fibich and Gavish \cite{BFGpd10}. We also prove the stability of these dynamics among radially symmetric solutions.
DOI:10.48550/arxiv.2406.04422