We consider the semilinear wave equation ${\partial }_t^{2}u-\Delta u=f\left(u\right),(x,t)\in {\mathbb{R}}^N\times [0,T),\left(1\right)$ with $f\left(u\right)={\left|u\right|}^{p-1}u{log}^a(2+u^2)$, where $p>1$ and $a\in \mathbb{R}$, with subconformal power nonlinearity. We will show that the blow-up rate of any singular solution of (1) is given by the ODE solution associated with $\left(1\right)$, The result in one space dimension, has been proved in Hamza and Zaag (2020). Our goal here is to extend this result to higher dimensions.

中文翻译：

---

高维非标度不变半线性波动方程的膨胀率

我们考虑半线性波动方程 ${\partial }_{吨}^2你-\Delta 你=F\left(你\right),(X,吨)\in {\mathbb{电阻}}^N\times [0,吨),\left(1\right)$ 和 $F\left(你\right)={\left|你\right|}^{磷-1}你{日志}^{\mathrm{一种}}(2+{你}^2)$， 在哪里 $磷>1$ 和 $\mathrm{一种}\in \mathbb{电阻}$，具有次共形功率非线性。我们将证明 (1) 的任何奇异解的爆破率由与$\left(1\right)$, 一维空间的结果已在 Hamza 和 Zaag (2020) 中得到证明。我们的目标是将这个结果扩展到更高的维度。