9 citations · 29 across the 14 of their papers we have counts for
14 papers
A Structure-Preserving Numerical Scheme for Optimal Control and Design of Mixing in Incompressible Flows
Weiwei Hu, Ziqian Li, Yubiao Zhang +1
We develop a structure-preserving computational framework for optimal mixing control in incompressible flows. Our approach exactly conserves the continuous system's key invariants…
Periodic propagation of singularities for heat equations with time delay
Gengsheng Wang, Huaiqiang Yu, Yubiao Zhang
This paper presents two remarkable phenomena associated with the heat equation with a time delay: namely, the propagation of singularities and periodicity. These are manifested thr…
Sampling Observability for Heat Equations with Memory
Lingying Ma, Gengsheng Wang, Yubiao Zhang
This paper studies the sampling observability for the heat equations with memory in the lower-order term, where the observation is conducted at a finite number of time instants and…
Observability for heat equations with time-dependent analytic memory
Gengsheng Wang, Yubiao Zhang, Enrique Zuazua
This paper presents a complete analysis of the observability property of heat equations with time-dependent real analytic memory kernels. More precisely, we characterize the geomet…
Flow decomposition for heat equations with memory
Gengsheng Wang, Yubiao Zhang, Enrique Zuazua
We build up a decomposition for the flow generated by the heat equation with a real analytic memory kernel. It consists of three components: The first one is of parabolic nature; t…
Asymptotic observability identity for the heat equation in R^d
Gengsheng Wang, Ming Wang, Yubiao Zhang
We build up an asymptotic observability identity for the heat equation in the whole space. It says that one can approximately recover a solution, through observing it over some cou…
Observable set, observability, interpolation inequality and spectral inequality for the heat equation in
Gengsheng Wang, Ming Wang, Can Zhang +1
This paper studies connections among observable sets, the observability inequality, the Hölder-type interpolation inequality and the spectral inequality for the heat equation in $\…
Time optimal sampled-data controls for heat equations
Gengsheng Wang, Donghui Yang, Yubiao Zhang
In this paper, we first design a time optimal control problem for the heat equation with sampled-data controls, and then use it to approximate a time optimal control problem for th…
Observability and unique continuation inequalities for the Schrödinger equation
Gengsheng Wang, Ming Wang, Yubiao Zhang
In this paper, we present several observability and unique continuation inequalities for the free Schrödinger equation in the whole space. The observations in these inequalities ar…
Decompositions and bang-bang properties
Gengsheng Wang, Yubiao Zhang
In this paper, minimal time and minimal norm control problems are studied. The target sets considered are the origin of state spaces and controls are point-wisely bounded functions…
Unique continuation estimates for the Kolmogorov equation in the whole space
Yubiao Zhang
We prove in this Note an observation estimate at one point in time for the Kolmogorov equation in the whole space. Such estimate implies the observability and the null controllabil…
Impulse and sampled-data optimal control of heat equations, and error estimates
Emmanuel Trélat, Lijuan Wang, Yubiao Zhang
We consider the optimal control problem of minimizing some quadratic functional over all possible solutions of an internally controlled multi-dimensional heat equation with a perio…
Attainable subspaces and the bang-bang property of time optimal controls for heat equations
Gengsheng Wang, Yashan Xu, Yubiao Zhang
In this paper, we study two subjects on internally controlled heat equations with time varying potentials: the attainable subspaces and the bang-bang property for some time optimal…
Two equivalence theorems of different kinds of optimal control problems for Schrödinger equations
Y. Zhang
This paper builds up two equivalence theorems for different kinds of optimal control problems of internally controlled Schrödinger equations. The first one concerns with the equiva…