A remark on the finite-time blow-up for the critical heat equation in \(\mathbb {R}^N\)

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2026年6月12日

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Tahir Boudjeriou,
Patrizia Pucci,
Thin Van Nguyen

摘要

In this paper, we first establish a finite-time blow-up result for the Cauchy problem associated with a semilinear parabolic equation, involving a nonlinear term, with critical polynomial growth at infinity, under arbitrary positive initial energy. We then derive both lower and upper bounds for the maximal existence time. These results complement and improve the ones presented in Ishiwata et al. [7].