Classification of Blow-ups and Monotonicity Formula for Half Laplacian Nonlinear Heat Equation

Bin Deng, Yannick Sire, Juncheng Wei +1

We consider the nonlinear half laplacian heat equation $$u_t+(-\Delta {)}^{\frac{1}{2}}u-|u{|}^{p-1}u=0,{\mathbb{R}}^n\times (0,T).$$ We prove that all blows-up are type I, provided…