Sharp Lifespan Dichotomies and Threshold Phenomena for Semilinear Heat Equations Driven by the Logarithmic Laplacian

Huyuan Chen, Rui Chen, Daniel Hauer +1

We investigate nonnegative mild solutions of ${\partial }_{t}u+(-\Delta {)}^{\ln }u=f(u)$ in $(0,T)\times {\mathbb{R}}^N$, with initial datum $u(0,\cdot )=\mu u_0$, $\mu >0$. Unlike the classical and frac…