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Global Exact Boundary Controllability of a Class of Quasilinear Hyperbolic Systems of Conservation Laws II

De-Xing Kong, Hui Yao
2005 SIAM Journal of Control and Optimization  
AE É ½ É ¾ É ª ½ ª ¾ ª ª É ¿ É ª ª ¿ ª È ª ½¼ È ½ È È ¾ È ¿ ª Ç ª ÙÖ ½ ÓÑ Ò× ª ´ ½ ¡ ¡ ¡ ½¼µ Ö Ø Ö ×Ø × ½´Ø µ È ½ È Ü ½´Ø µ ÇÈ ¾ Ü ¾´Ø µ È ¾ È ¿ Ü ¾´Ø µ  ...  µ Ö Å × Ú Ò Ý Å Ñ Ü Þ ¼ Ì ½ ¾¨ Ê ´Ù Þ´Ü µ Ú Þ´Ü µ ¼´ ½ ¼ µ Ê ´Ù · Þ´Ü µ Ú · Þ´Ü µ ¼´ ¼ ½ µ © ´½º½ µ Ê Ñ Ö ª ½ Ò ÐÓ× Ý Ø Ö Ø Ö ×Ø × Ü Ü ½´Ø µ Ü Ü ¾´Ø µ Ò Ø Ü¹ Ü × ª ½ ´Ø ܵ ¼ Ø Ø Ô Ü ¾´Ø µ Ü Ü ½´Ø µ ´¾º  ... 
doi:10.1137/s0363012903432651 fatcat:364tsifjznen7pyqik7vvjezfa

Modeling, Control and Numerics of Gas Networks [article]

Martin Gugat, Michael Herty
2020 arXiv   pre-print
In this article we survey recent progress on mathematical results on gas flow in pipe networks with a special focus on questions of control and stabilization.  ...  We briefly present the modeling of gas flow and coupling conditions for flow through vertices of a network.  ...  Controllability The results about the exact boundary controllability of general one-dimensional quasilinear hyperbolic systems that have been obtained in the framework of classical solutions (see e.g.  ... 
arXiv:2010.02743v1 fatcat:jxfvtk23qjcv3ofj3cvuj7ttxm

Hyperbolic Conservation Laws

Constantine Dafermos, Dietmar Kröner, Randall LeVeque
2008 Oberwolfach Reports  
and viscous perturbations for a class of multidimensional systems of conservation laws.  ...  Boundary Values for Moment Equation Ingo Müller The moment equations of the kinetic theory of gases furnish a quasilinear hyperbolic system which is entirely explicit.  ...  It is also sometimes beneficial to introduce a magnetic potential, A, that is related to the magnetic field in the following way: The ideal MHD equations form a system of hyperbolic conservation laws,  ... 
doi:10.4171/owr/2008/56 fatcat:vwgkrt2egzgr3krlmfhngtxm4i

Local exact one-sided boundary null controllability of entropy solutions to a class of hyperbolic systems of balance laws [article]

Tatsien Li, Lei Yu
2017 arXiv   pre-print
We prove the local exact one-sided boundary null controllability of entropy solutions to this class of systems, which generalizes the corresponding results from the case without source terms to that with  ...  We consider nxn hyperbolic systems of balance laws in one-space dimension under the assumption that all negative (resp. positive) characteristics are linearly degenerate.  ...  In [18] , we obtained the local exact one-sided boundary null controllability of entropy solutions to a class of quasilinear hyperbolic systems of conservation laws ∂ t H(u) + ∂ x F (u) = 0, t ≥ 0, 0  ... 
arXiv:1711.08582v2 fatcat:qbjxypzvmfemxpqc4ikeeoasce

Boundary Feedback Control of 2x2 Quasilinear Hyperbolic Systems: Predictive Synthesis and Robustness Analysis [article]

Timm Strecker, Ole Morten Aamo, Michael Cantoni
2021 arXiv   pre-print
We present a predictive feedback control method for a class of quasilinear hyperbolic systems with one boundary control input.  ...  Rigorous, although conservative conditions on the time derivative of the initial condition and on the design parameter controlling the convergence speed are given to ensure global existence of the solution  ...  The exact, finite time boundary controllability and observability of 1-dimensional hyperbolic systems is well established for both linear [4] and quasilinear [5] , [6] , [7] systems.  ... 
arXiv:2104.04581v1 fatcat:sebjmzmimndbzfiztdre62y3xa

Null controllability and finite-time stabilization in minimal time of one-dimensional first-order 2 × 2 linear hyperbolic systems [article]

Long Hu, Guillaume Olive
2020 arXiv   pre-print
The goal of this article is to present the minimal time needed for the null controllability and finite-time stabilization of one-dimensional first-order 2 × 2 linear hyperbolic systems.  ...  The main technical point is to show that we cannot obtain a better time. The proof combines the backstepping method with the Titchmarsh convolution theorem.  ...  This project was supported by National Natural Science Foundation of China (No. 12071258) and the Young Scholars Program of Shandong University (No. 2016WLJH52).  ... 
arXiv:2010.15664v1 fatcat:llpewpxwrrf3nhnphawz6dnzga

Two-point boundary value problems and exact controllability for several kinds of linear and nonlinear wave equations [article]

De-Xing Kong, Qing-You Sun
2010 arXiv   pre-print
In this paper we introduce some new concepts for second-order hyperbolic equations: two-point boundary value problem, global exact controllability and exact controllability.  ...  exact controllability of these wave equations.  ...  This work was supported in part by the NNSF of China (Grant No. 10971190) and the Qiu-Shi Chair Professor Fellowship from Zhejiang University.  ... 
arXiv:0910.5782v2 fatcat:w5ysibalofefvpv7nyl3qq7fem

List of contents

2003 Applied Mathematics Letters  
Wang Spiral Flames Collectively Fixed-Point Theorems in Noncompact G-Convex Spaces A Note on "Well-Posedness Theory for Hyperbolic Conservation Laws" Comparison of Numerical Schemes for Solving  ...  Muiioz Rivera 243 of Positive Solutions to a Quasilinear Eliptic System and Blow-Up Estimates for a Non-Newtonian Filtration System D. Xie, Y. Sheng and X.  ... 
doi:10.1016/s0893-9659(03)90138-8 fatcat:sgh4wgebmnfchpedljenuojy2m

J. M. Ball,(ed) Systems of nonlinear partial differential equations (D. Reidel, Dordrecht, 1983), ix + 481 pp., Dfl. 150

B. D. Sleeman
1984 Proceedings of the Edinburgh Mathematical Society  
One of its most interesting applications is the recent work of R. Diperna of global existence for some 2x2 systems of conservation laws with bounded data.'  ...  Tartar motivates these ideas through the equations of electrostatics and makes application to hyperbolic systems of conservation laws satisfying certain entropy conditions.  ... 
doi:10.1017/s0013091500022343 fatcat:lut7cbmhlvevfmr54sdhkkbugi

Exact controllability of wave equations on a circle [article]

De-Xing Kong, Qing-You Sun
2010 arXiv   pre-print
In this paper, we investigate the two-point boundary value problems for linear wave equation defined on a circle and prove that the equation possesses the exact controllability.  ...  We also investigate the two-point boundary value problems for the wave equation defined on a strip with Dirichlet or Neumann boundary conditions and show that the equation still possesses the exact controllability  ...  This work was supported in part by the NNSF of China (Grant No. 10971190) and the Qiu-Shi Chair Professor Fellowship from Zhejiang University.  ... 
arXiv:0912.5018v2 fatcat:exh3tz5bmjafndgi3oh4arajri

Multidimensional Conservation Laws: Overview, Problems, and Perspective [chapter]

Gui-Qiang G. Chen
2011 IMA Volumes in Mathematics and its Applications  
Some basic features and phenomena of multidimensional hyperbolic conservation laws are revealed, and some samples of multidimensional systems/models and related important problems are presented and analyzed  ...  Some of recent important developments are overviewed, several longstanding open problems are discussed, and a perspective is presented for the mathematical theory of multidimensional conservation laws.  ...  Hyperbolic Conservation Laws, quasilinear hyperbolic systems in divergence form, are one of the most important classes of nonlinear partial differential equations (PDEs for short).  ... 
doi:10.1007/978-1-4419-9554-4_2 fatcat:dirygzolwvdv5pbn22osofrfdq

Multidimensional Conservation Laws: Overview, Problems, and Perspective [article]

Gui-Qiang G. Chen
2010 arXiv   pre-print
Some basic features and phenomena of multidimensional hyperbolic conservation laws are revealed, and some samples of multidimensional systems/models and related important problems are presented and analyzed  ...  Some of recent important developments are overviewed, several longstanding open problems are discussed, and a perspective is presented for the mathematical theory of multidimensional conservation laws.  ...  The work of Gui-Qiang G.  ... 
arXiv:1008.1752v1 fatcat:bylfwm4nlzbd5imhcfhghb5kcq

Boundary conditions for the gravitational field

Jeffrey Winicour
2012 Classical and quantum gravity  
At present, it is known how to treat boundaries in the harmonic formulation of Einstein's equations and a tetrad formulation of the Einstein-Bianchi system.  ...  A review of the treatment of boundaries in general relativity is presented with the emphasis on application to the formulations of Einstein's equations used in numerical relativity.  ...  The results were further generalized in [18, 19] to apply to a general quasilinear class of symmetric hyperbolic systems whose boundary conditions have a certain hierarchical form.  ... 
doi:10.1088/0264-9381/29/11/113001 fatcat:wkcgyir3g5finozefuhslsalju

Euler Equations and Related Hyperbolic Conservation Laws [chapter]

Gui-Qiang Chen
2005 Handbook of Differential Equations: Evolutionary Equations  
Global well-posedness for discontinuous solutions, including the BV theory and the L ∞ theory, for the one-dimensional Euler equations and related hyperbolic systems of conservation laws is described.  ...  Some aspects of recent developments in the study of the Euler equations for compressible fluids and related hyperbolic conservation laws are analyzed and surveyed.  ...  Hyperbolic Conservation Laws, quasilinear hyperbolic systems in divergence form, are one of the most important classes of nonlinear partial differential equations, which typically take the following form  ... 
doi:10.1016/s1874-5717(06)80004-6 fatcat:ojye7odrs5d25atmtgu2ustphq

Solutions for Models of Chemically Reacting Mixtures [chapter]

Vincent Giovangigli
2016 Handbook of Mathematical Analysis in Mechanics of Viscous Fluids  
The hyperbolic-parabolic structure of the resulting system of partial differential equations is analyzed using symmetrizing variables.  ...  The situations of traveling waves and reaction-diffusion systems is also addressed.  ...  Global existence and uniform boundedness for a class of boundary value problems for binary reaction-diffusion systems has been investigated by Hollis, Martin and Pierre [65] .  ... 
doi:10.1007/978-3-319-10151-4_73-1 fatcat:hicjev26mjdvdo7hkkt2wkmg5y
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