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arXiv · 2504.10383

A monotonicity formula for a semilinear fractional parabolic equation

Ignacio Bustamante
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Abstract

We apply a high-dimensional parabolic-to-elliptic transformation to the fully fractional, semilinear heat equation $(\partial_t -\Delta)^s u = |u|^{p-1}u$, where $0 1$, and establish a monotonicity formula for the corresponding extension problem. This result serves as a fractional analogue of the Giga-Kohn monotonicity formula for the local equation $\partial_t u - \Delta u = |u|^{p-1}u.$ The method of proof may be applicable to other nonlinear and nonlocal settings.

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Ignacio Bustamante. 2025-04-14. A monotonicity formula for a semilinear fractional parabolic equation. https://doi.org/10.1016/j.na.2026.114224

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