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Control of systems of conservation laws with boundary errors
1.  LAASCNRS, University of Toulouse, 7, avenue du Colonel Roche, 31077 Toulouse, France 
[1] 
Xavier Litrico, Vincent Fromion, Gérard Scorletti. Robust feedforward boundary control of hyperbolic conservation laws. Networks & Heterogeneous Media, 2007, 2 (4) : 717731. doi: 10.3934/nhm.2007.2.717 
[2] 
Mapundi K. Banda, Michael Herty. Numerical discretization of stabilization problems with boundary controls for systems of hyperbolic conservation laws. Mathematical Control & Related Fields, 2013, 3 (2) : 121142. doi: 10.3934/mcrf.2013.3.121 
[3] 
JeanMichel Coron, Matthias Kawski, Zhiqiang Wang. Analysis of a conservation law modeling a highly reentrant manufacturing system. Discrete & Continuous Dynamical Systems  B, 2010, 14 (4) : 13371359. doi: 10.3934/dcdsb.2010.14.1337 
[4] 
Afaf Bouharguane. On the instability of a nonlocal conservation law. Discrete & Continuous Dynamical Systems  S, 2012, 5 (3) : 419426. doi: 10.3934/dcdss.2012.5.419 
[5] 
Serge Nicaise. Control and stabilization of 2 × 2 hyperbolic systems on graphs. Mathematical Control & Related Fields, 2017, 7 (1) : 5372. doi: 10.3934/mcrf.2017004 
[6] 
Xiaoyu Fu. Stabilization of hyperbolic equations with mixed boundary conditions. Mathematical Control & Related Fields, 2015, 5 (4) : 761780. doi: 10.3934/mcrf.2015.5.761 
[7] 
A. V. Fursikov. Stabilization for the 3D NavierStokes system by feedback boundary control. Discrete & Continuous Dynamical Systems, 2004, 10 (1&2) : 289314. doi: 10.3934/dcds.2004.10.289 
[8] 
Yinsong Bai, Lin He, Huijiang Zhao. Nonlinear stability of rarefaction waves for a hyperbolic system with Cattaneo's law. Communications on Pure & Applied Analysis, 2021, 20 (7&8) : 24412474. doi: 10.3934/cpaa.2021049 
[9] 
Stefano Bianchini. On the shift differentiability of the flow generated by a hyperbolic system of conservation laws. Discrete & Continuous Dynamical Systems, 2000, 6 (2) : 329350. doi: 10.3934/dcds.2000.6.329 
[10] 
Yanning Li, Edward Canepa, Christian Claudel. Efficient robust control of first order scalar conservation laws using semianalytical solutions. Discrete & Continuous Dynamical Systems  S, 2014, 7 (3) : 525542. doi: 10.3934/dcdss.2014.7.525 
[11] 
Zuowei Cai, Jianhua Huang, Liu Yang, Lihong Huang. Periodicity and stabilization control of the delayed Filippov system with perturbation. Discrete & Continuous Dynamical Systems  B, 2020, 25 (4) : 14391467. doi: 10.3934/dcdsb.2019235 
[12] 
Mohammad Akil, Ali Wehbe. Stabilization of multidimensional wave equation with locally boundary fractional dissipation law under geometric conditions. Mathematical Control & Related Fields, 2019, 9 (1) : 97116. doi: 10.3934/mcrf.2019005 
[13] 
Duy Phan, Lassi Paunonen. Finitedimensional controllers for robust regulation of boundary control systems. Mathematical Control & Related Fields, 2021, 11 (1) : 95117. doi: 10.3934/mcrf.2020029 
[14] 
Gilbert Peralta, Karl Kunisch. Interface stabilization of a parabolichyperbolic pde system with delay in the interaction. Discrete & Continuous Dynamical Systems, 2018, 38 (6) : 30553083. doi: 10.3934/dcds.2018133 
[15] 
Alberto Bressan, Graziano Guerra. Shiftdifferentiabilitiy of the flow generated by a conservation law. Discrete & Continuous Dynamical Systems, 1997, 3 (1) : 3558. doi: 10.3934/dcds.1997.3.35 
[16] 
Alberto Bressan, Khai T. Nguyen. Conservation law models for traffic flow on a network of roads. Networks & Heterogeneous Media, 2015, 10 (2) : 255293. doi: 10.3934/nhm.2015.10.255 
[17] 
Robert I. McLachlan, G. R. W. Quispel. Discrete gradient methods have an energy conservation law. Discrete & Continuous Dynamical Systems, 2014, 34 (3) : 10991104. doi: 10.3934/dcds.2014.34.1099 
[18] 
Julien Jimenez. Scalar conservation law with discontinuous flux in a bounded domain. Conference Publications, 2007, 2007 (Special) : 520530. doi: 10.3934/proc.2007.2007.520 
[19] 
Tong Yang, Fahuai Yi. Global existence and uniqueness for a hyperbolic system with free boundary. Discrete & Continuous Dynamical Systems, 2001, 7 (4) : 763780. doi: 10.3934/dcds.2001.7.763 
[20] 
K. T. Joseph, Philippe G. LeFloch. Boundary layers in weak solutions of hyperbolic conservation laws II. selfsimilar vanishing diffusion limits. Communications on Pure & Applied Analysis, 2002, 1 (1) : 5176. doi: 10.3934/cpaa.2002.1.51 
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