Exact controllability of the heat equation with bilinear control

This paper deals with exact controllability of bilinear heat equation. Namely, given the initial state, we would like to provide a class of target states that can be achieved through the heat equation at a finite time by applying multiplicative controls. For this end, an explicit control strategy is constructed. Simulations are provided. Copyright © 2015 John Wiley & Sons, Ltd.     

EXACT BOUNDARY CONTROLLABILITY OF 1-D NONLINEAR SCHRODINGER EQUATION

In this paper, the boundary control problem of a distributed parameter system described by the Schr(o)dinger equation posed on finite interval α≤ x ≤β:{iyt yxx |y|2y = 0,y(α,t) = h1(t),y(β,t) = h2(t) for t ＞ 0 (S)is considered. It is shown that by choosing appropriate control inputs (hj), (j = 1,2) one can always guide the system (S) from a given initial state ψ∈ Hs(α,β),(s ∈ R) to a terminal state ψ∈ Hs(α,β), in the time period [0, T]. The exact boundary controllability is obtained by considering a related initial value control problem of Schr(o)dinger equation posed on the whole line R. The discovered smoothing properties of Schr(o)dinger equation have played important roles in our approach; this may be the first step to prove the results on boundary controllability of (semi-linear) nonlinear Schr(o)dinger equation.     

Exact boundary controllability of the nonlinear Schrödinger equation

This paper studies the exact boundary controllability of the semi-linear Schrödinger equation posed on a bounded domain Ω⊂Rn with either the Dirichlet boundary conditions or the Neumann boundary conditions. It is shown that if

     

Exact boundary controllability of nodal profile for 1-D quasilinear wave equations

Based on the theory of semi-global C ² solution for 1-D quasilinear wave equations, the local exact boundary controllability of nodal profile for 1-D quasilinear wave equations is obtained by a constructive method, and the corresponding global exact boundary controllability of nodal profile is also obtained under certain additional hypotheses.     

河渠非定常流的精确边界能控性

借助于一阶拟线性双曲型方程组混合初边值问题的半整体C^1解理论对单个河道及弦状网络河道中的非定常流动分别讨论了在闸门边界条件下的精确边界能控性问题,并对在泄洪边界条件下的精确边界能控性进行了相应的讨论。     

Exact boundary controllability for non‐autonomous quasilinear wave equations

In this paper, we first show that quite different from the autonomous case, the exact boundary controllability for non‐autonomous wave equations possesses various possibilities. Then we adopt a constructive method to establish the exact boundary controllability for one‐dimensional non‐autonomous quasilinear wave equations with various types of boundary conditions. Finally, we apply the results to multi‐dimensional quasilinear wave equation with rotation invariance. Copyright © 2007 John Wiley & Sons, Ltd.     

一维绝热流方程组的精确边界能控性

利用一阶拟线性双曲组混合初边值问题的精确能控性理论,通过对边界速度或压强的控制,实现了一维绝热流方程组的精确边界能控性.     

Exact controllability of thermoelastic plate equation with memory

In this paper, we consider exact control problem for a coupled system of plate with Gurtin‐Pipkin equation. Using duality arguments, the problem is reduced to the obtention of suitable observability estimates for the dual system. Firstly, we obtain the observability inequality of the dual system by means of multiplier method. Then, we prove that the system is exactly controllable based on the Hilbert Unique Method.     

Global exact boundary controllability for 1‐D quasilinear wave equations

Based on the local exact boundary controllability for 1‐D quasilinear wave equations, the global exact boundary controllability for 1‐D quasilinear wave equations in a neighborbood of any connected set of constant equilibria is obtained by an extension method. Similar results are also given for a kind of general 1‐D quasilinear hyperbolic equations. Copyright © 2010 John Wiley & Sons, Ltd.     

Exact boundary controllability for 1‐D quasilinear wave equations with dynamical boundary conditions

By equivalently replacing the dynamical boundary condition by a kind of nonlocal boundary conditions, and noting a hidden regularity of solution on the boundary with a dynamical boundary condition, a constructive method with modular structure is used to get the local exact boundary controllability for 1‐D quasilinear wave equations with dynamical boundary conditions. Copyright © 2016 John Wiley & Sons, Ltd.     

高阶拟线性双曲型方程的精确边界能控性

By means of the existence and uniqueness of semi-global C^1 solution to the mixed initial-boundary value problem with general nonlinear boundary conditions for first order quasilinear hyperbolic systems with zero eigenvalues ,the local exact boundary controllability for higher order quasilinear hyperbolic equations is established.     

Exact controllability of the wave equation with time-dependent and variable coefficients

This paper deals with boundary exact controllability for the dynamics governed by the wave equation with variable coefficients in time and space, subject to Dirichlet or Neumann boundary controls. The observability inequalities are established by the Riemannian geometry method under some geometric conditions.     

Exact boundary controllability of a shallow intrinsic shell model

We consider a variant of a Koiter shell model based on the intrinsic geometry methods of Michael Delfour and Jean-Paul Zolésio. This model, derived in [J. Cagnol, I. Lasiecka, C. Lebiedzik, J.-P. Zolésio, Uniform stability in structural acoustic models with flexible curved walls, J. Differential Equations 186 (1) (2003) 88-121], relies heavily on the oriented distance function which describes the geometry. Here, we establish continuous observability estimates in the Dirichlet case with an explicit observability time, under an additional shallowness assumption and a checkable geometric condition. This yields (by duality) exact controllability for this class of intrinsically modelled shells.     

Exact boundary controllability for a kind of second‐order quasilinear hyperbolic systems and its applications

In this paper, by means of a constructive method based on the existence and uniqueness of the semi‐global C² solution, we establish the local exact boundary controllability for a kind of second‐order quasilinear hyperbolic systems. As an application, we obtain the one‐sided local exact boundary controllability for the first‐order quasilinear hyperbolic systems of diagonal form with boundary conditions in which the diagonal variables corresponding to the positive eigenvalues and those corresponding to the negative eigenvalues are decoupled. Copyright © 2009 John Wiley & Sons, Ltd.     

Exact boundary controllability of an integrodifferential equation

An integrodifferential equation of the Volterra type is considered under the action of anL ₂(0, T, L₂())-boundary control. By harmonic analysis arguments it is shown that the controllability results obtained in [17] for the underlying reference model associated with a trivial convolution kernel, carry over to the model under consideration without any smallness assumption concerning the memory kernel.     

Approximate boundary controllability for the system of linear elasticity

The approximate controllability for variable coefficients, isotropic, evolution elasticity system is considered. The appropriate unique continuation theorem for solutions of the system is stated. Copyright © 2004 John Wiley & Sons, Ltd.     

Exact boundary controllability for quasilinear wave equations in a planar tree-like network of strings

In this paper the local exact boundary controllability for quasilinear wave equations on a planar tree-like network of strings is established and the number of boundary controls is equal to the number of simple nodes minus 1.     

Improved upwind discretization of the advection equation

The simplest upwind discretization of the advection equation is only first‐order accurate in time and space and very diffusive. In this article, the first‐order upwind method is improved by changing its basis functions. The resulting scheme, called exponentially fitted, proves to be more accurate in both space and time. In addition, it inherits some qualitative behaviors of the advection equation. The proposed approach is able to be generalized for more complicated problems provided that appropriate relations between the fitting parameters of the method are imposed. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 773–787, 2014