10 papers · 1 filter
Shape Design for Degenerate Hyperbolic Equation with Degenerate Boundary and Its Application to Observability
Dong-Hui Yang, Yuanzhi Zhou
In this paper, we study the observability and controllability of a class of degenerate hyperbolic equations with a control region intersecting the degenerate set. Unlike the existi…
Shape Design for Degenerate Parabolic Equations with Degenerate Boundaries and Its Application to Boundary Observability
Dong-Hui Yang, Bao-Zhu Guo
In this study, we firstly establish the well-posedness of a degenerate parabolic equation under Dirichlet boundary conditions. Following this, we introduce a shape design problem,…
Null Controllability for Degenerate Parabolic Equations with Internal Control Applied on a Measurable Subset
Donghui Yang, Mengze Gu, Baozhu Guo +1
This work serves as a continuation of our preceding paper [28]. In that study, we presented a separable variable method to derive the Lebeau-Robbiano spectral inequality for a spec…
Approximation of Degenerate Hyperbolic Equations with Interior Degeneracy and Applications to Controllability
Dong-Hui Yang, Bao-Zhu Guo
In this paper, we establish the existence of solutions for a particular class of degenerate hyperbolic equations. Following this, we approximate these degenerate equations by emplo…
Some Key Properties of Eigenfunctions Linked to Degenerate Elliptic Differential Operators
Dong-Hui Yang, Bao-Zhu Guo
In this study, we address the eigenvalue problem given by: \begin{equation*} \begin{cases} -\Div (w\nabla u_i)=\la_iu_i &\text{in } \Om\subset \mathbb{R}^n,\\ u_i=0 &\text{on } \pt…
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 $…
Shape Design for a Class of Degenerate Parabolic Equations with Boundary Point Degeneracy and Its Application to Boundary Observability
Donghui Yang, Jie Zhong
We study a class of degenerate parabolic equations with boundary point degeneracy in dimensions N>=2 and investigate the associated boundary observability problem by means of shape…