论文标题
半线性结构阻尼波方程的临界指数
Critical exponent for semi-linear structurally damped wave equation of derivative type
论文作者
论文摘要
本文的主要目的是研究以非线性类型的非线性结构阻尼波方程：$$ u_ {tt} - ΔU+μ+μ（-Δ）^{σ/2} u_t = | u_t | u_t | u_t | u_t |^p，quad U（0，x）= u_0（x）= u_0（x） $μ> 0 $，$ n \ geq1 $，$σ\ in（0,2] $和$ p> 1 $。尤其是，我们将通过使用新的测试功能和适当的符号假设来证明全球弱解决方案的不存在，并在亚临界情况和关键情况下对初始数据进行适当的符号假设。
Main purpose of this paper is to study the following semi-linear structurally damped wave equation with nonlinearity of derivative type: $$u_{tt}- Δu+ μ(-Δ)^{σ/2} u_t= |u_t|^p,\quad u(0,x)= u_0(x),\quad u_t(0,x)=u_1(x),$$ with $μ>0$, $n\geq1$, $σ\in (0,2]$ and $p>1$. In particular, we are going to prove the non-existence of global weak solutions by using a new test function and suitable sign assumptions on the initial data in both the subcritical case and the critical case.
