6 papers
Decay estimates for the two-dimensional Beam equation with potentials
Shuangshuang Chen, Han Cheng, Zijun Wan +1
This paper establishes time decay estimates for the following two-dimensional beam (plate) equation with a decaying real-valued potential : \begin{equation*} \partial_t^2 u + (Î…
Pointwise estimates for the fundamental solutions of higher order Schrödinger equations in low odd dimensions
Han Cheng, Shanlin Huang, Tianxiao Huang +1
In this paper, we study the fundamental solution of the higher order Schrödinger equation \begin{equation*} \mathrm{i}\partial_t u(x,t) = \big((-Î)^m + V(x)\big)u(x,t), \quad t \…
The boundedness of wave operators for the Laplace operator with finite rank perturbations
Han Cheng, Shanlin Huang, Avy Soffer +1
This paper investigates the boundedness of wave operators for the Laplace operator with finite rank perturbations \begin{equation*} H=-Î+\sum\limits_{i=1}^N\langle\cdot\,, Ï…
The -boundedness of wave operators for higher order Schrödinger operator with zero singularities in low odd dimensions
Han Cheng, Avy Soffer, Zhao Wu +1
This paper investigates the -bounds of wave operators for higher-order Schrödinger operators on , with and real-valued decaying pote…
Pointwise estimates for the fundamental solutions of higher order schrödinger equations with finite rank perturbations
Xinyi Chen, Han Cheng, Shanlin Huang
This paper is dedicated to studying pointwise estimates of the fundamental solution for the higher order Schrödinger equation: % we investigate the fundamental solution of the hig…
Pointwise estimates for the fundamental solutions of higher order Schrödinger equations in odd dimensions II: high dimensional case
Han Cheng, Shanlin Huang, Tianxiao Huang +1
In this paper, for any odd and any integer with , we study the fundamental solution of the higher order Schrödinger equation \begin{equation*} \mathrm{i}\partia…