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arXiv · 2510.17718

Flat Standing Sphere Blow-up Solutions for the Nonlinear Heat Equation

Senhao Duan
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Abstract

In this paper, we prove the existence of a singular standing sphere blow-up solution for the nonlinear heat equation with radial symmetry. This solution develops a finite-time singularity on a fixed-radius sphere and exhibits a flat blow-up profile. Our construction refines the method developed by Merle and Zaag \cite{MZJEMS24} which reduces the infinite-dimensional dynamics to a finite-dimensional problem in radial case. The solution satisfies explicit asymptotics near the singular ring and remains regular elsewhere.

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Senhao Duan. 2025-10-20. Flat Standing Sphere Blow-up Solutions for the Nonlinear Heat Equation. https://arxiv.org/abs/2510.17718

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