Exact Controllability of linear KP-I equation
Chenmin Sun
证明了当控制输入加在垂直区域上时，线性KP-I方程的精确能控性。更一般地，我们得到了分数阶线性KPI方程保证能观性所需的最小色散。
We prove the exact controllability of linear KP-I equation if the control input is added on a vertical domain. More generally, we have obtained the least dispersion needed to insure observability for fractional linear KP I equation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
We provide necessary and sufficient geometric conditions for the exact controllability of the one-dimensional fractional free and fractional harmonic Schrödinger equations. The necessary and sufficient condition for the exact controllability of fractional free Schrödinger equations is derived from the Logvinenko-Sereda theorem and its quantitative version established by Kovrijkine, whereas the one for the exact controllability of fractional harmonic Schrödinger equations is deduced from an infinite dimensional version of the Hautus test for Hermite functions and the Plancherel-Rotach formula.
Exact controllability of the linear Zakharov-Kuznetsov equation
考虑矩形域上线性Zakharov-Kuznetsov方程的左Dirich-let边界控制.利用平坦性方法，我们证明了该方程的零能控性，并提供了一个解析可达状态空间。
Global exact controllability in infinite time of Schrödinger equation
本文研究了薛定谔方程的能控性问题。证明了系统在无限时间内对任意位置都是精确可控的。证明是基于多值函数的逆映射定理。我们还证明了该系统在下索伯列夫空间中有限时间不精确可控。
Exact controllability of wave equations on a circle
本文研究了定义在圆上的线性波动方程的两点边值问题，证明了该方程具有精确能控性。我们还研究了定义在带上的波动方程的两点边值问题，并证明了方程在Dirichlet或Neumann边界条件下仍具有精确能控性.参见arXiv：0910.5782v1
Exact controllability of a linear Korteweg-de Vries equation by the flatness approach
本文考虑有界区域上的线性Korteweg-de Vries方程的左Dirichlet边界控制问题.在过去的十年中，利用Carleman估计证明了这类系统的轨迹能控性.本文进一步利用平坦性方法建立了解析函数空间中的精确能控性.
Boundary controllability for the quasilinear wave equation
研究了高维拟线性波动方程的边界精确能控性。我们的主要工具是几何分析。我们得到了平衡点附近长时间解的存在性，证明了在某些几何条件下平衡点附近的局部精确能控性。然后，我们建立了全局精确可控性，以这样一种方式，准线性波动方程的状态从平衡在一个位置移动到平衡在另一个位置在某些几何条件下。分别研究了Dirichlet作用和Neumann作用。结果表明，精确能控性是黎曼度量的几何特征，由拟线性波动方程的系数和平衡点给出。基于黎曼度量的截面曲率，给出了精确能控性的一个判据.最后通过算例验证了该方法的全局精确能控性。
Exact Controllability of the Distributed System Governed by the Wave Equation with Memory
我们将考虑由具有记忆的波动方程所支配的分布系统的精确能控性。证明了该机械系统可以在有限时间内被驱动到静止，且分布控制函数的绝对值有界。在这种情况下，存储器内核是指数的线性组合。
Global exact controllability in infinite time of Schrödinger equation: multidimensional case
证明了多维薛定谔方程在无限时间内在薛定谔算子本征函数的有限个线性组合的任意点附近是精确可控的.我们证明，一般地，相对于势，线性化系统在无限时间内是可控的。应用逆映射定理，证明了该非线性系统的能控性。
Our purpose is to adapt the Hilbert Uniqueness Method by J.-L. Lions in the case of fractional diffusion-wave equations. The main difficulty is to determine the right shape for the adjoint system, suitable for the procedure of HUM.
Two-point boundary value problems and exact controllability for several kinds of linear and nonlinear wave equations
本文对二阶双曲型方程引入了一些新的概念：两点边值问题，整体精确能控性和精确能控性。对于物理和几何中的几类重要的线性和非线性波动方程，我们证明了两点边值问题光滑解的存在性，并证明了这些波动方程的整体精确能控性.特别地，我们研究了定义在闭曲线上的一维波动方程的两点边值问题，证明了光滑解的存在性，这意味着这类波动方程的精确能控性.在此基础上，我们研究了定义在带上的波动方程的两点边值问题，证明了方程在Dirichlet或Neumann边界条件下仍具有精确能控性.最后，作为应用，我们引入了双曲曲率流，得到了类似于著名的Gage和Hamilton关于平面曲线曲率流的定理的结果。
Well-posedness and exact controllability of the mass balance equations for an extrusion process
本文研究了食品挤压过程等温物理模型的适定性和精确能控性。该模型表达了挤出机腔室中的质量平衡，由双曲型偏微分方程（PDE）和非线性常微分方程（ODE）组成，其动力学描述了移动界面的演变。通过适当的坐标变换和不动点论证，证明了该耦合系统解的存在性、唯一性和正则性，并证明了该系统的精确能控性。
In this paper, we consider the exact boundary controllability and the exact boundary synchronization (by groups) for a coupled system of wave equations with coupled Robin boundary controls. Owing to the difficulty coming from the lack of regularity of the solution, we confront a bigger challenge than that in the case with Dirichlet or Neumann boundary controls. In order to overcome this difficulty, we use the regularity results of solutions to the mixed problem with Neumann boundary conditions by Lasiecka and Triggiani to get the regularity of solutions to the mixed problem with coupled Robin …
Exact Bounded Boundary Controllability to Rest for the Two-Dimensional Wave Equation
研究了二维波动方程振动的精确有界控制问题。控制力施加到膜的边界上，该边界位于平面上的区域中。控制的目标是驱动系统在有限的时间内休息。
Exact boundary controllability results for a multilayer Rao-Nakra sandwich beam
研究了多层Rao-Nakra夹层梁的边界能控性问题。该梁模型由一个瑞利梁和若干波动方程耦合而成。我们考虑所有的组合，夹紧和铰接的边界条件与控制施加到任何时刻或旋转角在一端的梁。我们证明了精确可控性的阻尼参数是足够小的。在无阻尼情况下，精确能控性在对系统中的参数没有任何限制的情况下成立。在每种情况下，最优控制时间是在$L^2(0,T)$控制的最优正则性空间中获得的。证明我们的主要结果的一个关键步骤是证明具有齐次边界条件和零边界观测的特征系统的零解的唯一性。
We address the problem of controllability of the MHD system in a rectangular domain with a control prescribed on the side boundary. We identify a necessary and sufficient condition on the data to be null controllable, i.e., can be driven to the zero state. We also show that the validity of this condition allows the states to be stirred to each other. If the condition is not satisfied, one can move from one state to another with the help of a simple shear external magnetic force.
We consider the 1D nonlinear Schrödinger equation with bilinear control. In the case of Neumann boundary conditions, local exact controllability of this equation near the ground state has been proved by Beauchard and Laurent in arXiv:1001.3288. In this paper, we study the case of Dirichlet boundary conditions. To establish the controllability of the linearised equation, we use a bilinear control acting through four directions: three Fourier modes and one generic direction. The Fourier modes are appropriately chosen so that they satisfy a saturation property. These modes allow to control approx…
$H^1$ local exact controllability of some one-dimensional bilinear Schr{ö}dinger equations
本文研究一维双线性薛定谔方程的局部精确可控性，在 H_0^1 中建立可控性，并利用磁场诱导的 Zeeman 效应实现周期 H^1 态的可控性，同时讨论开放问题。
The moment method is used to prove the exact controllability of a wide class of bidimensional linear dispersive PDE's posed on the two-dimensional torus $\mathbb{T}^{2}.$ The control function is considered to be acting on a small vertical and horizontal strip of the torus. Our results apply to several well-known models including some bidimesional extensions of the Benajamin-Ono and Korteweg-de Vries equations. As a by product, the exponential stabilizability with any given decay rate is also established in $H^{s}_{p}(\mathbb{T}^{2}),$ with $s\geq 0,$ by constructing an appropriated feedback co…
Finite-approximate controllability of evolution systems via resolvent-like operators
本文推广了一种变分方法来研究希尔伯特空间中半线性发展方程的近似能控性和有限维精确能控性（有限近似能控性）.利用类预解算子对线性发展方程的有限近似能控性给出了一个有用的刻画。我们还找到了一个控制，使除了近似可控性的要求，它确保有限维精确可控性。假设相应的线性化方程的近似能控性，得到了自然条件下半线性发展方程有限近似能控的充分条件.所得结果推广和延续了近年来关于这一问题的一些结果。热方程的应用进行了处理。
The article studies the exact controllability and the stability of the sixth order Boussinesq equation \[ u_{tt}-u_{xx}+βu_{xxxx}-u_{xxxxxx}+(u^2)_{xx}=f, \quad β=\pm1, \] on the interval $S:=[0,2π]$ with periodic boundary conditions. It is shown that the system is locally exactly controllable in the classic Sobolev space, $H^{s+3}(S)\times H^s(S)$ for $s\geq 0$, for "small" initial and terminal states. It is also shown that if $f$ is assigned as an internal linear feedback, the solution of the system is uniformly exponential decay to a constant state in $H^{s+3}(S)\times H^s(S)$ for $s\geq 0$…
Exact controllability is proven on a graph with cycle. The controls can be a mix of controls applied at the boundary and interior vertices. The method of proof first uses a dynamical argument to prove shape controllability and velocity controllability, thereby solving their associated moment problems. This enables one to solve the moment problem associated to exact controllability. In the case of a single control, either boundary or interior, it is shown that exact controllability fails.
On the Uniform Controllability of the Inviscid and Viscous Burgers-$α$ Systems
该研究针对无粘与有粘Burgers-$α$系统，通过返回法得到无粘系统的全局一致精确能控性，并结合局部精确能控与全局近似能控结果，推导出有粘系统到常值态的全局精确能控性。
Exact and optimal controllability for scalar conservation laws with discontinuous flux
本文讨论了一类具有间断通量的一维守恒律的最优控制问题，并给出了该问题的可达集。对于最优控制问题，我们首先证明了极小值的存在性，然后给出了计算极小值的算法，同样的方法也适用于计算初始数据控制。证明依赖于具有间断通量的守恒律的显式公式和特征的更精细性质。
Local exact one-sided boundary null controllability of entropy solutions to a class of hyperbolic systems of balance laws
本文考虑一维空间中的nxn双曲型平衡律方程组，假设方程组中的所有负（分别为）正）特性是线性退化的。我们证明了这类系统熵解的局部精确单侧边界零能控性，从而将相应的结果从无源项的情形推广到有源项的情形.为了应用求解守恒律的策略，我们对构造方法作了实质性的修改，分别对系统的正向和反向引入了两种不同的近似解.分别证明了它们的极限解在某种程度上是等价的。
In this paper, we study the exact controllability and stabilization of a system of two wave equations coupled by velocities with an internal, local control acting on only one equation. We distinguish two cases. In the first one, when the waves propagate at the same speed: using a frequency domain approach combined with multiplier technique, we prove that the system is exponentially stable when the coupling region satisfies the geometric control condition GCC. Following a result of Haraux ([11]), we establish the main indirect observability inequality. This results leads, by the HUM method, to …
On the small-time bilinear control of a nonlinear heat equation: global approximate controllability and exact controllability to trajectories
本文研究任意维环面上非线性热方程的双线性控制，在饱和假设下证明同号状态间的小时间近似可控性，并在一维情形下结合局部精确可控性结果，证明任意正状态到基态的小时间精确可控性。
Local exact controllability to constant trajectories for Navier-Stokes-Korteweg model
本文研究了环面上可压缩 Navier-Stokes-Korteweg 系统到常值轨迹的局部精确能控性，通过分析线性化方程控制性质及伴随方程能观性，利用 Carleman 估计实现了在任意小正时间且无几何条件下的控制。
In this paper, we discuss our recent works on the null-controllability, the exact controllability, and the stabilization of linear hyperbolic systems in one dimensional space using boundary controls on one side for the optimal time. Under precise and generic assumptions on the boundary conditions on the other side, we first obtain the optimal time for the null and the exact controllability for these systems for a generic source term. We then prove the null-controllability and the exact controllability for any time greater than the optimal time and for any source term. Finally, for homogeneous …
In this work, we use the classical moment method to find a practical and simple criterion to determine if a family of linearized Dispersive equations on a periodic domain is exactly controllable and exponentially stabilizable with any given decay rate in $H^{s}_{p}(\mathbb{T})$ with $s\in \mathbb{R}$. We apply these results to prove that the linearized Smith equation, the linearized dispersion-generalized Benjamin-Ono equation, the linearized fourth-order Schrödinger equation, and the Higher-order Schrödinger equations are exactly controllable and exponentially stabilizable with any given deca…
Exact Controllability for Stochastic Transport Equations
本文研究了随机迁移方程的精确能控性问题，通过对漂移项施加边界控制和对扩散项施加内部控制来实现.通过对偶性论证，该能控性问题可化为倒向随机迁移方程的能观性问题，并通过一个新的整体Carleman估计得到所需的能观性估计.此外，我们提出了一些结果缺乏精确可控性，这表明两个控制的行动是必要的。在某种程度上，这表明随机偏微分方程的可控性问题不同于确定性偏微分方程。
Exact boundary controllability for 1-D quasilinear hyperbolic systems with a vanishing characteristic speed
一般一阶拟线性双曲型方程组精确边界能控性的一般理论要求系统的特征速度不为零。本文讨论的精确边界能控性，当这不是这种情况下。作为主要结果的应用，给出了一些重要的模型.该策略使用返回方法，该方法允许在某些情况下恢复非零特征速度。
Remarks on global controllability for the shallow-water system with two control forces
本文讨论了一维区间上带摩擦项的可压缩Navier-斯托克斯方程。当边界控制作用于区间两端时，研究了具有一般初始条件的该方程的精确能控性。受Guerrero和Imanuvilov在\cite{GI}中关于粘性Burger方程的工作的启发，我们通过选择无旋数据和利用\cite{cpde,cras}中发展的有效速度的概念，证明了精确的全局能控性结果对任何时间$T$都不成立.
Controllability of quasi-linear Hamiltonian NLS equations
证明了圆上拟线性Hamilton NLS方程在小数据下的任意时间内的内能控性。我们使用的程序减少到常系数的零阶和HUM方法证明的可控性的线性化问题。然后，我们将Nash-Moser-Hörmander隐函数定理应用为黑盒。
Exact controllability of two-dimensional hydroelastic waves
本文研究了二维水弹性波在周期性条件下的精确可控性，证明在初始和终态数据较小时，系统在任意短时间内的可控性。
We prove exact controllability for quasi-linear Hamiltonian Schrödinger equations on tori of dimension greater or equal then two. The result holds true for sufficiently small initial conditions satisfying natural minimal regularity assumptions, provided that the region of control satisfies the geometric control condition.
Exact controllability to trajectories for entropy solutions to scalar conservation laws in several space dimensions
我们描述了一种新的方法，使我们能够获得的结果，精确可控的多维守恒律的轨迹的熵解的背景下，仅仅是一个非退化假设的流量和自然的几何条件。
In this paper, we study the controllability of a Schrödinger equation with mixed boundary conditions on disjoint subsets of the boundary: dynamic boundary condition of Wentzell type, and Dirichlet boundary condition. The main result of this article is given by new Carleman estimates for the associated adjoint system, where the weight function is constructed specially adapted to the geometry of the domain. Using these estimates, we prove the exact controllability of the system with a boundary control acting only in the part of the boundary where the Dirichlet condition is imposed. Also, we obta…
Exact controllability of stochastic parabolic equations with multiplicative noise
证明了带有限个模的乘性噪声的线性和半线性随机抛物型方程是精确零能控的。
Exact Controllability of Nonlinear Heat Equations in Spaces of Analytic Functions
利用Carleman估计可以建立非线性抛物型方程轨迹的可控性。然而，通过这种方法，并不清楚如何确定给定的函数是否确实是可达的。在Gevrey空间中，通过考虑一维非线性热方程，基于控制输入的直接方法研究了抛物型方程的可达状态.假设非线性部分是空间变量x、未知量y及其导数$\partial$ x y的解析函数。通过研究空间变量的非线性Cauchy问题和空间导数喷流与时间导数喷流之间的关系，得到了小初值和小终值下的精确能控性结果，该结果可推广为复平面上某个球上的解析函数. 2010年数学学科分类：35K40、93B05
Simultaneous global exact controllability of an arbitrary number of 1D bilinear Schrödinger equations
本文研究了在有界区间上具有双线性控制的任意个数\textsc{1d}线性薛定谔方程的系统。我们证明了这些$N$方程在大时间内的全局精确能控性。这个结果是有效的任意潜在的一般假设所考虑的粒子的偶极矩。因此，即使在单个粒子的情况下，该结果也扩展了现有文献。证明结合了本地精确控制有限的本征态的总和，证明与科伦的返回方法，一个全球性的近似可控性，证明与李雅普诺夫策略，和一个紧凑的参数。
Exact Boundary Observability and Controllability of the Wave Equation in an Interval with two Moving Endpoints
本文研究了两个端点作线性移动的区间上的波动方程。我们用级数公式给出了精确解，并证明了解的能量以$1/t$的速率衰减。我们还建立可观测性的结果，在一个或两个端点，在一个尖锐的时间。此外，利用Hilbert唯一性方法，我们得到了精确的边界能控性结果。
Local exact boundary controllability of entropy solutions to a class of hyperbolic systems of conservation laws
本文研究了一类常重线性退化双曲型守恒律组熵解的局部精确边界能控性。通过对原来用于经典解的策略进行必要的修改，证明了系统的双侧边界能控性、单侧边界能控性和双侧少控制能控性.我们的构造方法是基于半整体解的适定性，半整体解是由一般非线性边界条件下的混合初边值问题的$ \e $ -近似前沿跟踪解的极限以及$ \e $ -近似前沿跟踪解和熵解的一些性质构造的.
In this paper, we study the exact boundary controllability of the linear fourth-order Schrödinger equation, with variable physical parameters and clamped boundary conditions on a bounded interval. The control acts on the first spatial derivative at the left endpoint. We prove that this control system is exactly controllable at any time $T>0$. The proofs are based on a detailed spectral analysis and on the use of nonharmonic Fourier series.
Finer analysis of characteristic curves and its application to shock profile, exact and optimal controllability of a scalar conservation law with strict convex flux
本文考虑一维空间中具有严格凸通量的标量守恒律。本文的研究目标是两个问题。第一个问题是知道熵解的轮廓。尽管事实上，这是广泛研究在过去的几十年中，完整的配置文件的熵解决方案是没有很好地理解。第二个问题是精确能控性。对Burgers方程进行了研究，得到了长时间的部分结果.对于所有时间的能控性以及一般凸流的能控性是一个具有挑战性的问题。在一篇开创性的论文中，Dafermos引入了特征曲线，并得到了凸守恒律解的一些定性性质。本文进一步研究了这些特征曲线的精细性质。作为一个双产品，我们解决这两个问题，在完整的一般性。根据Lax - Oleinik，Joseph - Gowda的显式公式，目标函数必须满足某些必要条件.在本文中，我们证明它也是足够的。证明方法高度依赖于Lax-Oleinik给出的特征方法和显式公式，证明是构造性的。该方法允许以可跟踪的方式解决最优可控性问题。
This paper deals with the null controllability of a coupled parabolic system, which is Kuramoto-Sivashinsky-Korteweg-de Vries equation coupled with heat equation through first order derivative. More precisely, we prove the null controllability of the system with a single localized bilinear interior control acting on either of the components of the coupled system, and with a single periodic boundary control acting through zeroth order derivatives of either of the components. We employ the well-known moment method to study the controllability of the concerned system.
Controllability and Stabilizability of the Linearized Compressible Navier-Stokes System with Maxwell's Law
本文研究了带 Maxwell 定律的线性化可压缩 Navier-Stokes 系统在周期边界下的控制性质，通过局部内部控制和单一边界控制证明了时间足够大时的精确可控性，并利用 Gramian 方法实现了任意衰减速率的指数可镇定性。
Biorthogonal functions for complex exponentials and an application to the controllability of the Kawahara equation via a moment approach
本文利用复指数函数的双正交序列和矩方法，先证明周期域上Kawahara方程线性化系统的精确可控性，再结合不动点论证与Bourgain光滑性质得到完整系统的局部可控性。
Local exact Lagrangian controllability for 1D barotropic compressible Navier--Stokes equations
本文研究一维正压可压缩Navier--Stokes方程，通过构造作用于动量方程的外力，实现了在给定时间内将初始子区间内的流体粒子精确移动至目标子区间的局部拉格朗日能控性。
Exact boundary controllability and observability for first order quasilinear hyperbolic systems with a kind of nonlocal boundary conditions
本文建立了一类具有非局部边界条件的一阶拟线性双曲型方程组的半正则经典解理论，并在此基础上用构造性方法得到了相应的精确边界能控性和精确边界能观性.并以线性化的圣维南系统和一维线性波动方程为例，证明了边界控制和边界观测的数目都不能减少，从而得出了双曲系统在有环网络中的精确边界能控性一般不能实现的结论.
Weak controllability of second order evolution systems and applications
能控性与能观性是分布参数系统的重要性质，精确能观性与精确能控性的等价性一般成立。在本文中，我们定义了一个新的能控性概念，即弱能控性，它与弱能观性不等式有关，并给出了它们之间的等价性。
The purpose of this work is to investigate the exponential stability of a second order coupled wave equations by laplacian with one locally internal viscous damping. Firstly, using a unique continuation theorem combined with a Carleman estimate, we prove that our system is strongly stable without any geometric condition. Secondly, using a combination of the multiplier techniques and the frequency domain approach, we show that our system is exponentially stable under \textbf{(PMGC)} condition on the damping region without any restriction on wave propagation speed (i.e whether the two wave equat…
Local Exact Controllability to Stationary Solutions of a Semilinear Parabolic Equation
该研究针对带Dirichlet边界的拟线性多孔介质方程，证明当初值与稳态解的W^{1,n}_0(Ω)∩C(Ω̄)范数差足够小时，方程在有限时间内具备局部精确能控性，拓展了抛物方程能控性理论结果。
We consider the 1D linear Schr{ö}dinger equation, on a bounded interval, with Dirichlet boundary conditions and bilinear scalar control. The small-time local exact controllability around the ground state was proved in [BeaLau10], under an appropriate nondegeneracy assumption. Here, we work under a weaker nondegeneracy assumption and we prove the small-time local exact controllability in projection, around the ground state, with estimates on the control (depending linearly on the target) simultaneously in several spaces. These estimates are obtained at the level of the linearized system, thanks…
We consider the 3D Navier-Stokes system driven by an additive finite-dimensional control force. The purpose of this paper is to show how the approximate controllability of this system can be derived from the approximate controllability of the Euler system linearised around some suitable trajectory. The proof presented here is shorter than the previous ones obtained by Lie algebraic methods and gives some new information about the structure of the control. The dimension of the control space provided by this approach is larger, but it is still uniform with respect to the viscosity.
On the controllability and stabilization of the linearized Benjamin equation on a periodic domain
在这项工作中，我们研究的可控性和稳定性的线性化本杰明方程模型的单向传播的长波在两个流体系统中，较低的流体具有较大的密度是无限深的界面是受毛细作用。我们证明了在具有$s\geq0$的$H_{p}^{s}(\mathbb{T})$中，具有周期边界条件的线性化Benjamin方程对任意给定的衰减率都是精确可控和指数镇定的.
Small-time global exact controllability of the Navier-Stokes equation with Navier slip-with-friction boundary conditions
本文研究了Navier-斯托克斯方程的小时间全局精确能控性，包括零平衡态和弱轨线的精确能控性。我们考虑一个粘性不可压缩流体在一个光滑的有界区域内，无论是在二维或三维发展。这些控件仅位于边界的一小部分上，与其所有连接的组件相交。在边界的其余部分，流体服从Navier滑动摩擦边界条件。即使粘性边界层出现在这些不受控制的边界附近，我们证明了小时间的全局精确可控性。我们的分析依赖于与渐近边界层展开相结合的欧拉方程的可控性。仔细选择边界控制使我们能够保证剩余边界层具有良好的耗散特性，然后可以使用局部技术精确地消除剩余边界层。
A new look at the controllability cost of linear evolution systems with a long gaze at localized data
本文重新研究线性一阶演化系统的可控性代价，从ODE推广到多维PDE，重点分析局部化及半经典微局部化初始数据对代价的影响。
Local exact controllability for the 2 and 3-d compressible Navier-Stokes equations
本文的目的是给出二维和三维可压缩Navier-斯托克斯方程在定常目标轨迹上当控制作用于整个边界时的局部精确能控性结果。然后，我们的研究是基于一些线性化版本的系统，这是由于一个子系统的耦合项有点弱的分析伴随系统的可观性。在这一步中，我们在负索伯列夫空间中强烈使用Carleman估计。
Approximate and exact controllability of the continuity equation with a localized vector field
本文研究了人群模型中一类迁移型偏微分方程的能控性。我们感兴趣的是控制它的控制是一个向量场，代表扰动的速度，本地化的一个固定的控制集。我们证明，对于每个初始和最终的配置，一个可以转向近似一个到另一个与Lipschitz控制时，不受控制的动态允许跨越控制集。我们还表明，精确能控性只适用于控制的规律性较低，其中一个可能会失去相关的解决方案的唯一性。
Controllability issues for continuous-spectrum systems and ensemble controllability of Bloch Equations
本文研究了在静磁场中，在Larmor频率色散情况下，非相互作用半自旋系综的Bloch方程的可控性。该系统可以看作是具有连续谱的无限维双线性系统的原型，其可控性还没有得到很好的理解。我们提供了几个数学答案，与近似和精确可控性之间的歧视，有限时间或无限时间可控性：这个系统是不完全可控的有限时间$T$与有界控制的$L^2(0,T)$，但它是近似可控的$L^\infty$在有限时间与无界控制$L^{\infty}_{loc}([0,+\infty))$。此外，我们提出了显式控制实现的渐近精确可控性的自旋+1/2或-1/2的一致状态。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。