9 papers
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…
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…
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…
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…
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…
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…