9 papers · 1 filter
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,…
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…
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…
Approximation of Elliptic Equations with Interior Single-Point Degeneracy and Its Application to Weak Unique Continuation Property
Weijia Wu, Yaozhong Hu, Donghui Yang +1
This paper investigates the quantitative weak unique continuation property (QWUCP) for a class of high-dimensional elliptic equations with interior point degeneracy. First, we esta…
Quantitative uniqueness estimates for stochastic parabolic equations on the whole Euclidean space
Yuanhang Liu, Donghui Yang, Xingwu Zeng +1
In this paper, a quantitative estimate of unique continuation for the stochastic heat equation with bounded potentials on the whole Euclidean space is established. This paper gener…
The solvability and a Stackelberg-Nash game problem for degenerate elliptic equations
Yuanhang Liu, Weijia Wu, Donghui Yang +1
This study aims to investigate the functional properties of weak solution spaces and their compact embedding properties in relation to the Dirichlet problem associated with a speci…