论文标题
通过迭代论点炸毁Nakao问题的解决方案
Blow-up of solutions to Nakao's problem via an iteration argument
论文作者
论文摘要
在本文中，我们考虑了弱耦合系统的弱解决方案的爆炸行为，用于半连接阻尼的波动方程和$ \ Mathbb {r}^n $中的半线性波方程。这个问题是Nakao教授Nakao（Kyushu University）提出的所谓中Nakao的问题的一部分，以介绍指数$ P $和$ Q $之间的关键关系。通过将迭代方法应用于切片程序的无界乘数，我们即使在小数据中也证明了弱解决方案的弱解决方案。我们改善了与先前的研究相比，尤其是在较高维度的情况下的爆炸结果和上限估计值。
In this paper, we consider blow-up behavior of weak solutions to a weakly coupled system for a semilinear damped wave equation and a semilinear wave equation in $\mathbb{R}^n$. This problem is part of the so-called Nakao's problem proposed by Professor Mitsuhiro Nakao (Kyushu University) for a critical relation between the exponents $p$ and $q$. By applying an iteration method for unbounded multipliers with a slicing procedure, we prove blow-up of weak solutions for Nakao's problem even for small data. We improve the blow-up result and upper bound estimates for lifespan comparing with the previous research, especially, in higher dimensional cases.
