11 papers
On Controllability of a Class of N -dimensional Hyperbolic Equations with Internal Single-point Degeneracy
Donghui Yang, Weijia Wu
This paper explores the controllability of a class of N-dimensional hyperbolic equations featuring a single interior degenerate point. Firstly, we establish the well-posedness of t…
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…
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…
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…
Null controllability of two kinds of coupled parabolic systems with switching control
Yuanhang Liu, Weijia Wu, Donghui Yang
The focus of this paper is on the null controllability of two kinds of coupled systems including both degenerate and non-degenerate equations with switching control. We first estab…
Optimal Actuator Location of the Norm Optimal Controls for Degenerate Parabolic Equations
Yuanhang Liu, Weijia Wu, Donghui Yang
This paper focuses on investigating the optimal actuator location for achieving minimum norm controls in the context of approximate controllability for degenerate parabolic equatio…
Carleman estimates for degenerate parabolic equations with single interior point degeneracy and its applications
Yuanhang Liu, Yaozhong Hu, Weijia Wu +1
We study the controllability of a class of -dimensional degenerate parabolic equations with single interior point degeneracy. We employ the Galerkin method to prove the existenc…
Null controllability of n-dimensional parabolic equations degenerated on partial boundary
Weijia Wu, Yaozhong Hu, Hongli Sun +1
This paper extends the Carleman estimates to high dimensional parabolic equations with highly degenerate symmetric coefficients on a bounded domain of Lipschitz boundary and use th…
Observability Inequality from Measurable Sets and the Stackelberg-Nash Game Problem for Degenerate Parabolic Equations
Yuanhang Liu, Weijia Wu, Donghui Yang +1
In this study, we employ the established Carleman estimates and propagation estimates of smallness from measurable sets for real analytic functions, along with the telescoping seri…
Extremal properties of the first eigenvalue and the fundamental gap of a sub-elliptic operator
Hongli Sun, Weijia Wu, Donghui Yang
We consider the problems of extreming the first eigenvalue and the fundamental gap of a sub-elliptic operator with Dirichlet boundary condition, when the potential is subjected…
Observability inequality, the interpolation inequality and the spectral inequality for the degenerate parabolic equation in R
Yuanhang Liu, Weijia Wu, Donghui Yang
This paper investigates the interrelationships between the observability inequality, the Hölder-type interpolation inequality, and the spectral inequality for the degenerate parabo…