Global existences and asymptotic behavior for semilinear heat equation

Avy Soffer, Yifei Wu, Xiaohua Yao

In this paper, we consider the global Cauchy problem for the $L^2$-critical semilinear heat equations ${\partial }_{t}h=\Delta h\pm |h{|}^{\frac{4}{d}}h,$ with $h(0,x)=h_0$, where $h$ is an unkn…