Wang, Ke Exact boundary controllability for a kind of second-order quasilinear hyperbolic systems. (English) Zbl 1270.35301 Chin. Ann. Math., Ser. B 32, No. 6, 803-822 (2011). The author considers the exact boundary controllability for a kind of second-order quasilinear hyperbolic systems. Based on the existence and uniqueness of semi-global \(C^1\) solution and the local exact boundary controllability for first-order quasilinear hyperbolic systems, by as contractive method developed by T. Li [Controllability and observability for quasilinear hyberbolic systems. Beijing: Higher Education Press (2010; Zbl 1198.93003)], he obtained the local exact boundary controllability for this skind of second-order quasilinear hyperbolic systems. Reviewer: Jong Yeoul Park (Pusan) Cited in 7 Documents MSC: 35L53 Initial-boundary value problems for second-order hyperbolic systems 93B05 Controllability 35L50 Initial-boundary value problems for first-order hyperbolic systems Keywords:first-order quasilinear hyperbolic systems; second-order quasilinear hyperbolic systems Citations:Zbl 1198.93003 PDFBibTeX XMLCite \textit{K. Wang}, Chin. Ann. Math., Ser. B 32, No. 6, 803--822 (2011; Zbl 1270.35301) Full Text: DOI References: [1] Li, T. T., Exact boundary controllability for quasilinear wave equations, J. Comput. Appl. Math., 190, 2006, 127–135. · Zbl 1105.93013 · doi:10.1016/j.cam.2005.04.012 [2] Li, T. T., Controllability and Observability for Quasilinear Hyperbolic Systems, AIMS Series on Applied Mathematics, Vol. 3, American Institute of Mathematical Sciences & Higher Education Press, Springfield, Beijing, 2010. [3] Li, T. T. and Jin, Y., Semi-global C 1 solution to the mixed initial-boundary value problem for quasilinear hyperbolic systems, Chin. Ann. Math., 22B(3), 2001, 325–336. · Zbl 1005.35058 · doi:10.1142/S0252959901000334 [4] Li, T. T. and Rao, B. P., Local exact boundary controllability for a class of quasilinear hyperbolic systems, Chin. Ann. Math., 23B(2), 2002, 209–218. · Zbl 1184.35196 · doi:10.1142/S0252959902000201 [5] Li, T. T. and Rao, B. P., Strong (weak) exact controllability and strong (weak) exact observability for quasilinear hyperbolic systems, Chin. Ann. Math., 31B(5), 2010, 723–742. · Zbl 1206.35168 · doi:10.1007/s11401-010-0600-9 [6] Li, T. T. and Yu, L. X., Exact boundary controllability for 1-D quasilinear wave equations, SIAM J. Control Optim., 45, 2006, 1074–1083. · Zbl 1116.93021 · doi:10.1137/S0363012903427300 [7] Li, T. T. and Yu, W. C., Boundary Value Problems for Quasilinear Hyperbolic Systems, Duke Univ. Math. Ser. V, Duke Univ. Press, Durham, 1985. · Zbl 0627.35001 [8] Wang, K., Global exact boundary controllability for 1-D quasilinear wave equations, Math. Meth. Appl. Sci., 34, 2011, 315–324. · Zbl 1213.35290 · doi:10.1002/mma.1358 [9] Wang, Z. Q., Exact boundary controllability for nonautonomous quasilinear wave equations, Math. Meth. Appl. Sci., 30, 2007, 1311–1327. · Zbl 1121.93010 · doi:10.1002/mma.843 [10] Yao, M. S., Advanced Algebra (in Chinese), Fudan University Press, Shanghai, 2005. [11] Yu, L. X., Exact boundary controllability for second order quasilinear hyperbolic systems, Chin. J. Engin. Math., 22, 2005, 199–211. · Zbl 1134.93316 [12] Yu, L. X., Exact boundary controllability for a kind of second-order quasilinear hyperbolic systems and its applications, Math. Meth. Appl. Sci., 33, 2010, 273–286. · Zbl 1186.35109 [13] Zhuang, K. L. and Shang, P. P., Exact boundary controllability for second order quasilinear hyperbolic equations (in Chinese), Chin. J. Engin. Math., 26(6), 2009, 1005–1020. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.