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Exact Boundary Controllability for the Spatial Vibration of String with Dynamical Boundary Conditions

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Chinese Annals of Mathematics,Series B 2020年第3期41卷 325-334页

作者： Yue WANg günter.leugering Tatsien LI Department of Mathematics Friedrich-Alexander UniversityErlangen 91058GermanySchool of Mathematical SciencesFudan UniversityShanghai 200433China Department of Mathematics Friedrich-Alexander UniversityErlangen-NurembergCauerstrasse 1191058 ErlangenGermany School of Mathematical Sciences Fudan UniversityShajighai 200433ChinaShanghai Key Laboratory for Contemporary Applied MathematicNonlinear Mathematical Modeling and Methods Laboratory

This paper deals with the spatial vibration of an elastic string with masses at the endpoints. The authors derive the corresponding quasilinear wave equation with dynamical boundary conditions, and prove the exact bou... 详细信息

关键词： Spatial vibration of a string Exact boundary controllability Dynamical boundary condition

Exact Boundary Controllability on a Tree-Like Network of Nonlinear Planar Timoshenko Beams

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Chinese Annals of Mathematics,Series B 2017年第3期38卷 711-740页

作者： Qilong gU günter.leugering Tatsien LI School of Mathematical Sciences Shanghai Jiao Tong UniversityShanghai 200240China Department Mathematik Friedrich-Alexander University Erlangen-Nuremberg91058 ErlangenGermany School of Mathematical Sciences Fudan UniversityShanghai 200433China Shanghai Key Laboratory for Contemporary Applied Mathematics Nonlinear Mathematical Modeling and Methods Laboratory

This paper concerns a system of equations describing the vibrations of a planar network of nonlinear Timoshenko beams. The authors derive the equations and appropriate nodal conditions, determine equilibrium solutions and, using the methods of quasilinear hyperbolic systems, prove that for tree-like networks the natural initial-boundary value problem admits semi-global classical solutions in the sense of Li [Li, T. T., Controllability and Observability for Quasilinear Hyperbolic Systems, AIMS Ser. Appl. Math., vol 3,American Institute of Mathematical Sciences and Higher Education Press, 2010] existing in a neighborhood of the equilibrium solution. The authors then prove the local exact controllability of such networks near such equilibrium configurations in a certain specified time interval depending on the speed of propagation in the individual beams.

关键词： Timoshenko梁平面非线性树状网络边界能控性拟线性双曲型方程组高等教育出版社精确可控性数学科学

H^2-Stabilization of the Isothermal Euler Equations: a Lyapunov Function Approach

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Chinese Annals of Mathematics,Series B 2012年第4期33卷 479-500页

作者： Martin gUgAT günter.leugering Simona TAMASOIU Department of Mathematics Friedrich-Alexander University Erlangen-Nuremberg Cauerstrasse 11 91058 Erlangen Germany

The authors consider the problem of boundary feedback stabilization of the 1D Euler gas dynamics locally around stationary states and prove the exponential stability with respect to the H^2-norm. To this end, an explicit Lyapunov function as a weighted and squared H^2-norm of a small perturbation of the stationary solution is constructed. The authors show that by a suitable choice of the boundary feedback conditions, the H^2-exponential stability of the stationary solution follows. Due to this fact, the system is stabilized over an infinite time interval. Furthermore, exponential estimates for the C^1-norm are derived.

关键词： Lyapunov函数方法指数稳定 H2范数 Euler方程静止状态反馈镇定力学边界函数构造

AN AUgMENTED BV SETTINg FOr FEEDBACK SWITCHINg CONTrOL

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Journal of Systems Science & Complexity 2010年第3期23卷 456-466页

作者： Falk M.HANTE günter.leugering Thomas I.SEIDMAN Department Mathematik Lehrstuhl für Angewandte Mathematik ⅡUniversitt Erlangen-Nürnberg Department of Mathematics and Statistics University of Maryland Baltimore County

This paper considers dynamical systems under feedback with control actions limited *** authors wish to understand the closed-loop systems as approximating multi-scale problemsin which the implementation of switching merely acts on a fast *** hybrid dynamicalsystems are extensively studied in the literature,but not much so far for feedback with partial *** becomes in particular relevant when the dynamical systems are governed by partialdifferential *** authors introduce an augmented BV setting which permits recognition ofcertain fast scale effects and give a corresponding well-posedness result for observations with such *** an application for this setting,the authors show existence of solutions for systemsof semilinear hyperbolic equations under such feedback with pointwise observations.

关键词：开关控制 BV公司动反馈混合动力系统地点状态观测双曲型方程组多尺度问题

Domain Decomposition of an Optimal Control Problem for Semi-Linear Elliptic Equations on Metric graphs with Application to gas Networks

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Applied Mathematics 2017年第8期8卷 1074-1099页

作者： günter.leugering Chair of Applied Mathematics II Friedrich-Alexander-University Erlangen-Nuremberg Erlangen Germany

We consider optimal control problems for the flow of gas in a pipe network. The equations of motions are taken to be represented by a semi-linear model derived from the fully nonlinear isothermal Euler gas equations. We formulate an optimal control problem on a given network and introduce a time discretization thereof. We then study the well-posedness of the corresponding time-discrete optimal control problem. In order to further reduce the complexity, we consider an instantaneous control strategy. The main part of the paper is concerned with a non-overlapping domain decomposition of the semi-linear elliptic optimal control problem on the graph into local problems on a small part of the network, ultimately on a single edge.

关键词： Optimal Control gas Networks Euler’s Equation Hierarchy of Models Semi-Linear Approximation Non-Overlapping Domain Decomposition

On Henig regularization of Material Design Problems for Quasi-Linear p-Biharmonic Equation

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Applied Mathematics 2016年第14期7卷 1547-1570页

作者： Peter Kogut günter.leugering ralph Schiel Department of Differential Equations Dnipropetrovsk National University Dnipro Ukraine Department Mathematik Lehrstuhl II Universit&auml t Erlangen-Nürnberg Cauerstr Erlangen Germany

We study a Dirichlet optimal design problem for a quasi-linear monotone p-biharmonic equation with control and state constraints. We take the coefficient of the p-biharmonic operator as a design variable in . In this ... 详细信息

关键词： p-Biharmonic Problem Optimal Design relaxation Henig Dilating Cone Existence result