6 papers
Null Controllability for a Multi-Dimensional Degenerate Parabolic Equation with Degenerated Interior Point
Dong-Hui Yang, Bao-Zhu Guo, Jie Zhong
In this study, we study the null controllability of a multi-dimensional degenerate parabolic equation characterized by a degenerate interior point. The control domain, which is an…
Quantitative Weak Unique Continuation on Annular Domains for Backward Degenerate Parabolic Equations with Degenerate Interior Points
Dong-Hui Yang, Bao-Zhu Guo, Guojie Zheng +1
In this paper, we establish a quantitative weak unique continuation theorem on an annular domain for a backward degenerate parabolic equation with a degenerate interior point. Our…
A Shape Design Approximation for Degenerate Partial Differential Equations and Its Application
Bao-Zhu Guo, Dong-Hui Yang, Jie Zhong
In this paper, we focus on two types of degenerate partial differential equations: a degenerate elliptic equation and a degenerate parabolic equation. Significantly, both categorie…
Hidden Boundary Trace Regularity and an Observability Estimate with Interior Remainder for Boundary-Degenerate Hyperbolic Equations
Dong-Hui Yang, Jie Zhong
We study hidden boundary trace regularity for two-dimensional hyperbolic equations with boundary degeneracy governed by $\mcA\vp=-\Div(A\nabla \vp)$, where $A=\diag(1,r^\al)$ and $…
Observability inequalities for the backward stochastic evolution equations and their applications
Yuanhang Liu, Weijia Wu, Donghui Yang +1
The present article delves into the investigation of observability inequalities pertaining to backward stochastic evolution equations. We employ a combination of spectral inequalit…
Norm and time optimal control problems of stochastic heat equations
Yuanhang Liu, Donghui Yang, Jie Zhong
This paper investigates the norm and time optimal control problems for stochastic heat equations. We begin by presenting a characterization of the norm optimal control, followed by…