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math.AP2025
Sharp power concavity of two relevant free boundary problems of reaction-diffusion type
Qingyou He
The porous medium type reaction-diffusion equation and the Hele-Shaw problem are two free boundary problems linked through the incompressible (Hele-Shaw) limit. We investigate and…
math.AP2024
Porous medium type reaction-diffusion equation: large time behaviors and regularity of free boundary
Qingyou He
We consider the Cauchy problem of the porous medium type reaction-diffusion equation \begin{equation*} \partial_tρ=Δρ^m+ρg(ρ),\quad (x,t)\in \mathbb{R}^n\times \mathbb{R}_+,\quad n…