3 papers
math.AP2025
A Liouville theorem for supercritical Fujita equation and its applications
Kelei Wang, Juncheng Wei, Ke Wu
We prove a Liouville theorem for ancient solutions to the supercritical Fujita equation \[\partial_tu-Îu=|u|^{p-1}u, \quad -\infty <t<0, \quad p>\frac{n+2}{n-2},\] which says if $…
math.AP2025
Quantitative stratification for the fractional Allen-Cahn equation and stationary nonlocal minimal surface
Kelei Wang, Juncheng Wei, Ke Wu
We study properties of solutions to the fractional Allen-Cahn equation when and dimension . By applying the quantitative stratification principle developed…
math.AP2024
F-stability, entropy and energy gap for supercritical Fujita equation
Kelei Wang, Juncheng Wei, Ke Wu
We study some problems on self similar solutions to the Fujita equation when , especially, the characterization of constant solutions by the energy. Motivated by rec…