Journal Articles Discrete and Continuous Dynamical Systems - Series A Year : 2025

Standing-sphere blowup solutions for the nonlinear heat equation

Abstract

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 [BFG10]. We also prove the stability of these dynamics among radially symmetric solutions.
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Dates and versions

hal-04609030 , version 1 (12-06-2024)

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Senhao Duan, Nejla Nouaili, Hatem Zaag. Standing-sphere blowup solutions for the nonlinear heat equation. Discrete and Continuous Dynamical Systems - Series A, 2025, 45 (5), pp.1434-1453. ⟨10.3934/dcds.2024134⟩. ⟨hal-04609030⟩
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