具有无界阻尼的阻尼波方程的伪谱

热算子束的伪谱

Pseudospectra of the heat operator Pencil

该研究针对带左狄利克雷、右诺依曼边界条件的一维热方程，将其重构为非自伴2×2无界块算子矩阵束，通过分析其谱、伪谱及(n,ε)-伪谱包络研究热算子束，并辅以离散化方程图像验证结果。

The damped wave equation with unbounded damping

We analyze new phenomena arising in linear damped wave equations on unbounded domains when the damping is allowed to become unbounded at infinity. We prove the generation of a contraction semigroup, study the relation between the spectra of the semigroup generator and the associated quadratic operator function, the convergence of non-real eigenvalues in the asymptotic regime of diverging damping on a subdomain, and we investigate the appearance of essential spectrum on the negative real axis. We further show that the presence of the latter prevents exponential estimates for the semigroup and t…

Instability results for the damped wave equation in unbounded domains

We extend some previous results for the damped wave equation in bounded domains in Euclidean spaces to the unbounded case. In particular, we show that if the damping term is of the form $αa$ with bounded $a$ taking on negative values on a set of positive measure, then there will always exist unbounded solutions for sufficiently large positive $α$. In order to prove these results, we generalize some existing results on the asymptotic behaviour of eigencurves of one-parameter families of Schrodinger operators to the unbounded case, which we believe to be of interest in their own right.

具有无界阻尼的一维阻尼波方程的预解式估计

Resolvent estimates for the one-dimensional damped wave equation with unbounded damping

本文研究了具有无界阻尼的一维阻尼波方程生成元 $G$，证明了其预解算子范数在复左半平面有界宽度垂直条带上趋于常数，核心方法是对二次算子逆范数的精确渐近分析。