Refined Regularity of the Blow-Up Set Linked to Refined Asymptotic Behavior for the Semilinear Heat Equation
Tej‐Eddine Ghoul, Nguyen Van Tien, Hatem Zaag · DOAJ (DOAJ: Directory of Open Access Journals) · 2017
We consider u(x,t)${u(x,t)}$, a solution of ∂tu=Δu+|u|p-1u${\partial_{t}u=\Delta u+|u|^{p-1}u}$ which blows up at some time T>0${T>0}$, where u:ℝN×[0,T)→ℝ${u:\mathbb{R}^{N}\times[0,T)\to\mathbb{R}}$, p>1${p>1}$ and (N-2)p 0${\mu>0}$. Knowing the refined asymptotic behavior yields geometric constraints of the blow-up set, leading to more regularity on S.