Exact Boundary Controllability for Quasilinear Wave Equations in a Planar Tree-Like Network of Strings
Annales de l'I.H.P. Analyse non linéaire, Volume 26 (2009) no. 6, p. 2373-2384
@article{AIHPC_2009__26_6_2373_0,
     author = {Gu, Qilong and Li, Tatsien},
     title = {Exact Boundary Controllability for Quasilinear Wave Equations in a Planar Tree-Like Network of Strings},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {26},
     number = {6},
     year = {2009},
     pages = {2373-2384},
     doi = {10.1016/j.anihpc.2009.05.002},
     zbl = {1180.35326},
     mrnumber = {2569899},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2009__26_6_2373_0}
}
Gu, Qilong; Li, Tatsien. Exact Boundary Controllability for Quasilinear Wave Equations in a Planar Tree-Like Network of Strings. Annales de l'I.H.P. Analyse non linéaire, Volume 26 (2009) no. 6, pp. 2373-2384. doi : 10.1016/j.anihpc.2009.05.002. http://www.numdam.org/item/AIHPC_2009__26_6_2373_0/

[1] Ammari K., Jellouli M., Stabilization of Star-Shaped Networks of Strings, Differential Integral Equations 17 (2004) 1395-1410. | MR 2100033 | Zbl 1150.93537

[2] Ammari K., Jellouli M., Remark on Stabilization of Tree-Shaped Networks of Strings, Appl. Math. 52 (2007) 327-343. | MR 2324731 | Zbl 1164.93315

[3] Ammari K., Jellouli M., Khenissi M., Stabilization of Generic Trees of Strings, J. Dyn. Control Syst. 11 (2005) 177-193. | MR 2131807 | Zbl 1064.93034

[4] Dáger R., Zuazua E., Wave Propagation, Observation and Control in 1-D Flexible Multi-Structures, Math. Appl., vol. 50, 2000. | Zbl 1083.74002

[5] Emanuilov O. Yu., Boundary Control by Semilinear Evolution Equations, Russian Math. Surveys 44 (1989) 183-184. | MR 1024065 | Zbl 0713.93030

[6] Lagnese J. E., Leugering G., Schmidt E. J.P. G., Modeling, Analysis and Control of Multi-Link Structures, Systems Control Found. Appl., Birhäuser-Basel, 1994. | Zbl 0810.73004

[7] Lasiecka I., Triggiani R., Exact Controllability of Semilinear Abstract Systems With Applications to Waves and Plates Boundary Control Problems, Appl. Math. Optim. 23 (1991) 109-154. | MR 1086465 | Zbl 0729.93023

[8] Li Tatsien, Jin Yi, Semi-Global C 1 Solution to the Mixed Initial-Boundary Value Problem for Quasilinear Hyperbolic Systems, Chinese Ann. Math. Ser. B 22 (2001) 325-336. | MR 1845753 | Zbl 1005.35058

[9] Li Tatsien, Rao Bopeng, Exact Boundary Controllability for Quasilinear Hyperbolic Systems, SIAM J. Control Optim. 41 (2003) 1748-1755. | Zbl 1032.35124

[10] Li Tatsien, Rao Bopeng, Local Exact Boundary Controllability for a Class of Quasilinear Hyperbolic Systems, Chinese Ann. Math. Ser. B 23 (2002) 209-218. | MR 1924137 | Zbl pre01799638

[11] Li Tatsien, Yu Lixin, Contrôlabilité Exacte Frontière Pour Les Équations Des Ondes Quasi Linéaires Unidimensionnelles, C. R. Acad. Sci. Paris Sér. I 337 (2003) 271-276. | MR 2009120 | Zbl 1029.93036

[12] Li Tatsien, Yu Lixin, Exact Boundary Controllability for 1-D Quasilinear Wave Equations, SIAM J. Control Optim. 45 (2006) 1074-1083. | MR 2247726 | Zbl 1116.93021

[13] Li Tatsien, Yu Wenci, Boundary Value Problems for Quasilinear Hyperbolic Systems, Duke Univ. Math. Ser., vol. V, 1985. | Zbl 0627.35001

[14] Lions J.-L., Contrôlabilité Exacte, Perturbations Et Stabilisation De Systèmes Distribués, Vol. I, Masson, 1988. | Zbl 0653.93003

[15] Lions J.-L., Exact Controllability, Stabilization and Perturbations for Distributed Systems, SIAM Rev. 30 (1988) 1-68. | MR 931277 | Zbl 0644.49028

[16] Nicaise S., Valein J., Stabilization of the Wave Equation on 1-D Networks With a Delay Term in the Nodal Feedbacks, Netw. Heterog. Media 2 (2007) 425-479, (electronic). | MR 2318841 | Zbl pre05232638

[17] Russell D. L., Controllability and Stabilizability Theory for Linear Partial Differential Equations, Recent Progress and Open Questions, SIAM Rev. 20 (1978) 639-739. | MR 508380 | Zbl 0397.93001

[18] Schmidt E. J.P. G., On the Modeling and Exact Controllability of Networks of Vibrating Strings, SIAM J. Control Optim. 30 (1992) 229-245. | MR 1145715 | Zbl 0755.35008

[19] Zuazua E., Exact Controllability for the Semilinear Wave Equation, J. Math. Pures Appl. 69 (1990) 1-31. | MR 1054122 | Zbl 0638.49017

[20] Zuazua E., Exact Controllability for Semilinear Wave Equations, Ann. Inst. H. Poincaré Anal. Non Linéaire 10 (1993) 109-129. | Numdam | MR 1212631 | Zbl 0769.93017

[21] Zuazua E., Controllability of Partial Differential Equations and Its Semi-Discrete Approximation, Discrete Contin. Dyn. Syst. 8 (2002) 469-513. | MR 1897693 | Zbl 1005.35019