论文标题
尖锐的多项式衰变，用于多个以上的奇异阻尼
Sharp polynomial decay for polynomially singular damping on the torus
论文作者
论文摘要
我们研究了阻尼波动方程的能量衰减速率，并没有几何控制条件，而无限制阻尼。我们的主要衰减结果是尖锐的多项式能量衰减，用于在圆环上多项式控制的奇异阻尼。我们还证明，对于正常$ l^p $ damp的紧凑型歧管，Schrödinger可观察性会产生$ p $依赖性的多项式衰减，并且不会发生有限的时间灭绝。我们表明，圆上多项式控制的奇异阻尼会产生指数衰减。
We study energy decay rates for the damped wave equation with unbounded damping, without the geometric control condition. Our main decay result is sharp polynomial energy decay for polynomially controlled singular damping on the torus. We also prove that for normally $L^p$-damping on compact manifolds, the Schrödinger observability gives $p$-dependent polynomial decay, and finite time extinction cannot occur. We show that polynomially controlled singular damping on the circle gives exponential decay.
