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arXiv · 1910.05502

Energy Non-collapsing and Refined Blowup for a Semilinear Heat Equation

Shi-Zhong Du
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Abstract

Refined structures of blowup for non-collapsing maximal solution to a semilinear parabolic equation are studied. We will prove that the blowup set is empty for non-collapsing blowing-up in subcritical case, and all finite time non-collapsing blowing-up must be type II in critical case. When p>p_S=(N+2)/(N-2) for N>=3, the Hausdorff dimension of the blowup set for maximal solution whose energy is non-collapsing is shown to be no greater than N-2-4/(p-1), which answers a question proposed in [7] positively. At the end of this paper, we also present some new examples of collapsing and non-collapsing blowups.

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Shi-Zhong Du. 2019-10-12. Energy Non-collapsing and Refined Blowup for a Semilinear Heat Equation. https://doi.org/10.1016/j.jde.2018.10.047

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