Shanlin Huang

activity

20152024

collaborators

6 papers

math.AP2024

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 $n$ and any integer $m \geq 1$ with $n > 4 m$ , we study the fundamental solution of the higher order Schrödinger equation \begin{equation*} \mathrm{i}\partial…

math.CA2023

Heisenberg Uniqueness Pairs and the wave equation

Shanlin Huang, Jiaqi Yu

Given a curve $Γ$ and a set $Λ$ in the plane, the concept of the Heisenberg uniqueness pair $(Γ, Λ)$ was first introduced by Hedenmalm and Motes-Rodr\'ıgez (Ann. of Math. 173(2),15…

math.AP2022

Dispersive estimates for the Schrödinger equation with finite rank perturbations

Han Cheng, Shanlin Huang, Quan Zheng

In this paper, we investigate dispersive estimates for the time evolution of Hamiltonians $$ H=-Δ+\sum_{j=1}^N\langle\cdot\,, φ_j\rangle φ_j\quad\,\,\,\text{in}\,\,\,\mathbb{R}^d,\…

math.AP2020

Characterizations of stabilizable sets for some parabolic equations in $R^{n}$

Shanlin Huang, Gengsheng Wang, Ming Wang

We consider the parabolic type equation in $R^{n}$ : \begin{align}\label{equ-0} (\partial_t+H)y(t,x)=0,\,\,\, (t,x)\in (0,\infty)\times\mathbb{R}^n;\;\; \quad y(0,x)\in L^2(\…

math.OC2020

Observable sets, potentials and Schrödinger equations

Shanlin Huang, Gengsheng Wang, Ming Wang

We characterize observable sets for 1-dim Schrödinger equations in $R$ : $i \partial_{t} u = (- \partial_{x}^{2} + x^{2 m}) u$ (with $m \in N := {0, 1, \dots}$ ). More precisely,…

math.AP2015

Quantitative uniqueness of some higher order elliptic equations

Shanlin Huang, Ming Wang, Quan Zheng

We study the quantitative unique continuation property of some higher order elliptic operators. In the case of $P = (- Δ)^{m}$ , where $m$ is a positive integer, we derive lower bounds o…