论文标题
中Nakao类型问题的爆炸和寿命估计值与衍生品类型的非线性
Blow-up and lifespan estimates for Nakao's type problem with nonlinearities of derivative type
论文作者
论文摘要
在本文中，我们调查了一类半线性双曲线耦合系统的爆炸和寿命估计，其中$ \ m \ m mathbb {r}^n $带有$ n \ geqslant 1 $，这是所谓的Nakao Nakao的类型问题的一部分，这些问题与半潮湿的波浪等方程式与半度性趋于deribine tyble等方程式相关。通过构建两个时间依赖的功能，并采用切片程序的无界乘数进行迭代方法，得出了能量解决方案寿命的爆破和上限估计的结果。该模型似乎是双曲线状的，而不是类似抛物线的。特别是，一维情况的爆炸结果是最佳的。
In the present paper, we investigate blow-up and lifespan estimates for a class of semilinear hyperbolic coupled system in $\mathbb{R}^n$ with $n\geqslant 1$, which is part of the so-called Nakao's type problem weakly coupled a semilinear damped wave equation with a semilinear wave equation with nonlinearities of derivative type. By constructing two time-dependent functionals and employing an iteration method for unbounded multiplier with slicing procedure, the results of blow-up and upper bound estimates for the lifespan of energy solutions are derived. The model seems to be hyperbolic-like instead of parabolic-like. Particularly, the blow-up result for one dimensional case is optimal.
