Author

Zhi-Wen Duan

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Preprint Sep 2026

Observability Inequalities and the Logvinenko--Sereda Theorem for the Dunkl Transform

Let $R$ be a normalized root system in $\mathbb{R}^d$ with reflection group $G$, let $k$ be a $G$-invariant multiplicity function, and let $\mathcal{F}_k$ be the associated Dunkl transform. We write $k_\alpha=k(\alpha)>0$ and $\mathrm{d}\mu_k(x)=w(x)\,\mathrm{d}x$, where $w(x)=\prod_{\alpha\in R_+}|\langle x,\alpha\ran...

Xing-Yu Zhao, Long Wei, Zhi-Wen Duan · 0 citations

Apr 2022

Dispersive decay for the nonlinear magnetic Schrödinger equation

In this paper, we obtain the dispersive estimates and global well-posedness of the nonlinear magnetic Schr\"odinger equation in $\mathbb{R}^{3}$ with nonlinearity $|u|^{p-1}u$ with exponent $\frac{5}{3}<p<5$ when the initial value stays in a suitable space $\Sigma_{s}$. By proving the resolvent estimates with weight fu...

Lei Wei, Zhi-Wen Duan · Nonlinear Analysis · 1 citation · ⚡1

Preprint Sep 2026

Double-logarithmic stability for a parabolic inverse problem on CTA manifolds

We establish a double-logarithmic stability estimate for the recovery of a time-dependent potential in the parabolic equation $(c^{-1}\partial_t-\Delta_g+q)u=0$ on a conformally transversally anisotropic manifold. The partial input--output map associates an initial state and lateral Dirichlet data supported in a prescr...

Yu-Jian Zheng, Zhi-Wen Duan, Shi-Qi Jing · 0 citations