论文标题
超临界半线性热方程的临界规范的爆炸
Blow-up of the critical norm for a supercritical semilinear heat equation
论文作者
论文摘要
我们考虑到半线性加热方程的爆炸解决方案的缩放标准$ u_t =ΔU+| u | |^{p-1} u $在$ \ mathbf {r}^n $的任意平滑域中。在$ p> p_s的范围内：=（n+2）/（n-2）$，我们表明必须在不施加I型I爆炸条件的爆炸时间附近无限制。鉴于存在具有$ p = p_s $的II型爆炸解决方案的存在，范围$ p> p_s $是最佳的。
We consider the scaling critical Lebesgue norm of blow-up solutions to the semilinear heat equation $u_t=Δu+|u|^{p-1}u$ in an arbitrary smooth domain of $\mathbf{R}^n$. In the range $p>p_S:=(n+2)/(n-2)$, we show that the critical norm must be unbounded near the blow-up time, where the type I blow-up condition is not imposed. The range $p>p_S$ is optimal in view of the existence of type II blow-up solutions with bounded critical norm for $p=p_S$.
