论文标题
一维阻尼波方程的分解估计值无界阻尼
Resolvent estimates for the one-dimensional damped wave equation with unbounded damping
论文作者
论文摘要
我们研究具有无限阻尼的一维阻尼波方程的发电机$ g $。我们表明，相应的回答操作员的规范，$ \ | （g-λ）^{ - 1} \ | $，大约是$ |λ| \ to +\ to +\ infty $上的垂直宽度条上包含在左侧宽度的宽度宽度，$ \ overline {\ MathBb {c}} _ { - } _ { - }：= \ \ {λ\ in \ in \ in \ in \ Mathbb {c}：\ opererorname：\ opertorname}我们的证明基于对与$ g $相关的二次操作员$ t（λ）$倒数的准确渐近分析。
We study the generator $G$ of the one-dimensional damped wave equation with unbounded damping. We show that the norm of the corresponding resolvent operator, $\| (G - λ)^{-1} \|$, is approximately constant as $|λ| \to +\infty$ on vertical strips of bounded width contained in the closure of the left-hand side complex semi-plane, $\overline{\mathbb{C}}_{-} := \{λ\in \mathbb{C}: \operatorname{Re} λ\le 0\}$. Our proof rests on a precise asymptotic analysis of the norm of the inverse of $T(λ)$, the quadratic operator associated with $G$.
