13 citations · 45 across the 19 of their papers we have counts for
19 papers
A logarithmic convexity approach to quantitative unique continuation for the complex Ginzburg-Landau operator
Yueliang Duan, Borui Liu, Can Zhang
We establish quantitative unique continuation estimates for solutions of the complex Ginzburg-Landau equation in the framework of two-sphere and one-cylinder inequalities. While pr…
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…
Quantitative unique continuation for parabolic equations with Neumann boundary conditions
Yueliang Duan, Lijuan Wang, Can Zhang
In this paper, we establish a globally quantitative estimate of unique continuation at one time point for solutions of parabolic equations with Neumann boundary conditions in bound…
Quantitative unique continuation and observability on an equidistributed set for the diffusion equation in R^N
Yueliang Duan, Huaiqiang Yu, Can Zhang
In this paper, we obtain a quantitative estimate of unique continuation and an observability inequality from an equidistributed set for solutions of the diffusion equation in the w…
A uniform bound on costs of controlling semilinear heat equations on a sequence of increasing domains and its application
Lijuan Wang, Can Zhang
In this paper, we first prove a uniform upper bound on costs of null controls for semilinear heat equations with globally Lipschitz nonlinearity on a sequence of increasing domains…
Observability inequalities for the heat equation with bounded potentials on the whole space
Yueliang Duan, Lijuan Wang, Can Zhang
In this paper we establish an observability inequality for the heat equation with bounded potentials on the whole space. Roughly speaking, such a kind of inequality says that the t…
Minimal time impulse control of the heat equation
Yueliang Duan, Lijuan Wang, Can Zhang
The paper is concerned with a kind of minimal time control problem for the heat equation with impulse controls. The purpose of such a problem is to find an optimal impulse control…
Interpolation inequality at one time point for parabolic equations with time-independent coefficients and applications
Huaiqiang Yu, Can Zhang
In this paper, we study the Hölder-type interpolation inequality and observability inequality from measurable sets in time for parabolic equations either with L^p unbounded potenti…
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 $\…
Observability inequalities on measurable sets for the Stokes system and applications
Felipe W. Chaves-Silva, Diego A. Souza, Can Zhang
In this paper, we establish spectral inequalities on measurable sets of positive Lebesgue measure for the Stokes operator, as well as an observability inequalities on space-time me…
Quantitative unique continuation for the heat equation with Coulomb potentials
Can Zhang
In this paper, we establish a Hölder-type quantitative estimate of unique continuation for solutions to the heat equation with Coulomb potentials in either a bounded convex domain…
Optimal shape design for 2D heat equations in large time
Emmanuel Trelat, Can Zhang, Enrique Zuazua
In this paper, we investigate the asymptotic behavior of optimal designs for the shape optimization of 2D heat equations in long time horizons. The control is the shape of the doma…
Integral and measure-turnpike properties for infinite-dimensional optimal control systems
Emmanuel Trelat, Can Zhang
We first derive a general integral-turnpike property around a set for infinite-dimensional non-autonomous optimal control problems with any possible terminal state constraints, und…
Steady-state and periodic exponential turnpike property for optimal control problems in Hilbert spaces
Emmanuel Trelat, Can Zhang, Enrique Zuazua
In this work, we study the steady-state (or periodic) exponential turnpike property of optimal control problems in Hilbert spaces. The turnpike property, which is essentially due t…
Analyticity of solutions to parabolic evolutions and applications
Luis Escauriaza, Santiago Montaner, Can Zhang
We find new quantitative estimates on the space-time analyticity of solutions to linear parabolic equations with analytic coefficients near the initial time. We apply the estimates…
Observability inequalities from measurable sets for some evolution equations
Gengsheng Wang, Can Zhang
In this paper, we build up two observability inequalities from measurable sets in time for some evolution equations in Hilbert spaces from two different settings. The equation read…
Unique Continuation and Observability Estimates for 2-D Stokes Equations with the Navier Slip Boundary Condition
Yuning Liu, Can Zhang
This paper presents a unique continuation estimate for 2-D Stokes equations with the Naiver slip boundary condition in a bounded and simply connected domain. Consequently, an obser…
Observability Inequalities and Measurable Sets
J. Apraiz, L. Escauriaza, G. Wang +1
This paper presents two observability inequalities for the heat equation over . In the first one, the observation is from a subset of positive measure in $Ω\times(0,T…
The time optimal control problem with control constraints of the rectangular type for a class of ODEs
Can Zhang
This paper studies a time optimal control problem with control constraints of the rectangular type for the linear multi-input time-varying ordinary differential equations. The aims…