论文标题
与Glassey猜想相关的空间相关类型的关键阻尼项的波动方程的爆炸和寿命估计值
Blow-up and lifespan estimate for wave equations with critical damping term of space-dependent type related to Glassey conjecture
论文作者
论文摘要
本文的主要目的是研究波动方程的爆炸问题，并在\ textit {scale-castimist案例}中使用空间依赖性阻尼和带有小初始数据的时间导数非线性。 Under appropriate initial data which are compactly supported, by using a test function method and taking into account the effect of the damping term ($\fracμ{\sqrt{1+|x|^2}}u_t$), we provide that in higher dimensions the blow-up region is given by $p \in (1, p_G(N+μ)]$ where $p_G(N)$ is the Glassey exponent.此外，我们将建立一个爆炸区域，独立于$ p \ in（1，1+ \ frac {2} {n}），$用于在能量空间中提供适当的初始数据，并提供非策略支持。
The main purpose of the present paper is to study the blow-up problem of the wave equation with space-dependent damping in the \textit{scale-invariant case} and time derivative nonlinearity with small initial data. Under appropriate initial data which are compactly supported, by using a test function method and taking into account the effect of the damping term ($\fracμ{\sqrt{1+|x|^2}}u_t$), we provide that in higher dimensions the blow-up region is given by $p \in (1, p_G(N+μ)]$ where $p_G(N)$ is the Glassey exponent. Furthermore, we shall establish a blow-up region, independent of $μ$ given by $p\in (1, 1+\frac{2}{N}),$ for appropriate initial data in the energy space with noncompact support.
