论文标题
在较高维度的非缩放半线性波方程的爆炸率
The blow-up rate for a non-scaling invariant semilinear wave equations in higher dimensions
论文作者
论文摘要
我们考虑半连续波方程$ \ partial_t^2 u-Δu= f（u），\ quad（x，t）\ in \ mathbb r^n \ times [0，t），\ qquad（qquad（1）$ with $ f（u f（u f（u）= | | | | |^| |^{p -1） r $，具有亚符号功率非线性。 我们将证明（1）的任何单数解的爆炸率是由与$（1）$相关的ODE解决方案（在一个空间维度中的结果）给出的，已在\ cite {hzjmaa2020}中证明。我们的目标是将此结果扩展到更高的维度。
We consider the semilinear wave equation $$\partial_t^2 u -Δu =f(u), \quad (x,t)\in \mathbb R^N\times [0,T),\qquad (1)$$ with $f(u)=|u|^{p-1}u\log^a (2+u^2)$, 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 $(1)$, The result in one space dimension, has been proved in \cite{HZjmaa2020}. Our goal here is to extend this result to higher dimensions.
