27 citations · 37 across the 9 of their papers we have counts for
9 papers
Simultaneous recoveries for semilinear parabolic systems
Yi-Hsuan Lin, Hongyu Liu, Xu Liu +1
In this paper, we study inverse boundary problems associated with semilinear parabolic systems in several scenarios where both the nonlinearities and the initial data can be unknow…
Determining a nonlinear hyperbolic system with unknown sources and nonlinearity
Yi-Hsuan Lin, Hongyu Liu, Xu Liu
We investigate inverse boundary problems associated with a time-dependent semilinear hyperbolic equation, where both nonlinearity and sources (including initial displacement and in…
Verifiable constraint qualifications for infinite-dimensional optimization problems and their applications to optimal control problems
Xu Liu, Qi Lü, Haisen Zhang +1
This paper employs a finite codimensionality condition to establish an enhanced Fritz John condition for general constrained nonlinear infinite-dimensional optimization problems. I…
Finite Codimensional Controllability, and Optimal Control Problems with Endpoint State Constraints
Xu Liu, Qi Lü, Xu Zhang
In this paper, motivated by the study of optimal control problems for infinite dimensional systems with endpoint state constraints, we introduce the notion of finite codimensional…
Finite Codimensional Controllability for Evolution Equations
Xu Liu, Qi Lu, Xu Zhang
Motivated by infinite-dimensional optimal control problems with endpoint state constraints, in this Note, we introduce the notion of finite codimensional exact controllability for…
An Internal Observability Estimate for Stochastic Hyperbolic Equations
Xiaoyu Fu, Xu Liu, Qi Lu +1
This paper is addressed to establishing an internal observability estimate for some linear stochastic hyperbolic equations. The key is to establish a new global Carleman estimate f…
A weighted identity for stochastic partial differential operators and its applications
Xiaoyu Fu, Xu Liu
In this paper, a pointwise weighted identity for some stochastic partial differential operators (with complex principal parts) is established. This identity presents a unified appr…
On the equivalence between local and global existence of complete Kähler metrics with plurisubharmonic potentials
Xu Liu
Like the classical potential theory, it was conjectured that there exists equivalence between locally and globally pluripolar and complete pluripolar sets, namely, Problem I of Lel…
Calderon-Type Uniqueness Theorem for Stochastic Partial Differential Equations
Xu Liu, Xu Zhang
In this Note, we present a Calderón-type uniqueness theorem on the Cauchy problem of stochastic partial differential equations. To this aim, we introduce the concept of stochastic…