论文标题
在所有维度中的能量强调波动方程的自相似解决方案
Self-similar solutions of energy-supercritical focusing wave equations in all dimensions
论文作者
论文摘要
在本文中，我们证明了一个可数的常规球体对称的自相似解的存在，以聚焦能量超临界半线性波方程\ begin {quation*} \ partial_ {tt} u-Δu= | u |^{p-1} u \ qquad \ qquad \ text {in} \，\，\，\，\ mathbb {r}^{n}，\ end end {equication {equation*} $ p \ leq 1+ \ frac {4} {n-3} $。以前仅在$ n = 3 $的情况下知道这一点，对于整数$ p $（请参阅Bizoń，Maison和Wasserman \ cite {BMW}）。我们还研究了这些解决方案的渐近学。
In this paper, we prove the existence of a countable family of regular spherically symmetric self-similar solutions to focusing energy super-critical semi-linear wave equations \begin{equation*} \partial_{tt}u-Δu=|u|^{p-1}u \qquad \text{in} \,\, \mathbb{R}^{N}, \end{equation*} where $N\geq 3$, $1+\frac{4}{N-2}<p$, and, if $N\geq 4$, $p \leq 1+\frac{4}{N-3}$. This was previously known only in the case $N=3$, for integer $p$ (see Bizoń, Maison and Wasserman \cite{BMW}). We also study the asymptotics of these solutions.
