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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 483053, 6 pages
Boundary Controllability of a Pseudoparabolic Equation
1School of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou 510275, China
2School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China
Received 24 May 2013; Revised 29 July 2013; Accepted 30 July 2013
Academic Editor: Valery Y. Glizer
Copyright © 2013 Qiang Tao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- G. I. Barenblatt, I. P. Zheltov, and I. N. Kochina, “Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks,” Journal of Applied Mathematics and Mechanics, vol. 24, pp. 1286–1303, 1960.
- B. D. Coleman, R. J. Duffin, and V. J. Mizel, “Instability, uniqueness and nonexistence theorems for the equation on a strip,” Archive for Rational Mechanics and Analysis, vol. 19, pp. 100–116, 1965.
- T. W. Ting, “Certain non-steady flows of second-order fluids,” Archive for Rational Mechanics and Analysis, vol. 14, pp. 1–26, 1963.
- P. J. Chen and M. E. Gurtin, “On a theory of heat conduction involving two temperatures,” Zeitschrift für Angewandte Mathematik und Physik, vol. 19, pp. 614–627, 1968.
- V. Padrón, “Effect of aggregation on population revovery modeled by a forward-backward pseudoparabolic equation,” Transactions of the American Mathematical Society, vol. 356, no. 7, pp. 2739–2756, 2004.
- T. B. Benjamin, J. L. Bona, and J. J. Mahony, “Model equations for long waves in nonlinear dispersive systems,” Philosophical Transactions of the Royal Society of London A, vol. 272, no. 1220, pp. 47–78, 1972.
- V. Barbu, “Controllability of parabolic and Navier-Stokes equations,” Scientiae Mathematicae Japonicae, vol. 56, no. 1, pp. 143–211, 2002.
- A. Doubova, E. Fernández-Cara, M. González-Burgos, and E. Zuazua, “On the controllability of parabolic systems with a nonlinear term involving the state and the gradient,” SIAM Journal on Control and Optimization, vol. 41, no. 3, pp. 798–819, 2002.
- E. Fernández-Cara and E. Zuazua, “Null and approximate controllability for weakly blowing up semilinear heat equations,” Annales de l'Institut Henri Poincaré. Analyse Non Linéaire, vol. 17, no. 5, pp. 583–616, 2000.
- C. Fabre, J.-P. Puel, and E. Zuazua, “Approximate controllability of the semilinear heat equation,” Proceedings of the Royal Society of Edinburgh A, vol. 125, no. 1, pp. 31–61, 1995.
- A. V. Fursikov and O. Yu. Imanuvilov, Controllability of Evolution Equations, Seoul University, Seoul, Republic of Korea, 1996.
- X. Zhang, “A remark on null exact controllability of the heat equation,” SIAM Journal on Control and Optimization, vol. 40, no. 1, pp. 39–53, 2001.
- G. Wang, “-null controllability for the heat equation and its consequences for the time optimal control problem,” SIAM Journal on Control and Optimization, vol. 47, no. 4, pp. 1701–1720, 2008.
- S. Guerrero and O. Y. Imanuvilov, “Remarks on non controllability of the heat equation with memory,” ESAIM. Control, Optimisation and Calculus of Variations, vol. 19, no. 1, pp. 288–300, 2013.
- A. Doubova and E. Fernández-Cara, “On the control of viscoelastic Jeffreys fluids,” Systems & Control Letters, vol. 61, no. 4, pp. 573–579, 2012.
- J. L. Boldrini, A. Doubova, E. Fernández-Cara, and M. González-Burgos, “Some controllability results for linear viscoelastic fluids,” SIAM Journal on Control and Optimization, vol. 50, no. 2, pp. 900–924, 2012.
- M. A. Shubov, “Exact boundary and distributed controllability of radial damped wave equation,” Journal de Mathématiques Pures et Appliquées, vol. 77, no. 5, pp. 415–437, 1998.
- A. López, X. Zhang, and E. Zuazua, “Null controllability of the heat equation as singular limit of the exact controllability of dissipative wave equations,” Journal de Mathématiques Pures et Appliquées. Neuvième Série, vol. 79, no. 8, pp. 741–808, 2000.
- F. W. Chaves-Silva, L. Rosier, and E. Zuazua, “Null controllability of a system of viscoelasticity with a moving control,” Journal de Mathématiques Pures et Appliquées, 2013.
- A. Münch and E. Zuazua, “Numerical approximation of null controls for the heat equation: Ill-posedness and remedies,” Inverse Problems, vol. 26, no. 8, Article ID 085018, 39 pages, 2010.
- R. E. Showalter, “Partial differential equations of Sobolev-Galpern type,” Pacific Journal of Mathematics, vol. 31, pp. 787–793, 1969.
- R. E. Showalter and T. W. Ting, “Pseudoparabolic partial differential equations,” SIAM Journal on Mathematical Analysis, vol. 1, pp. 1–26, 1970.
- S. Micu, “On the controllability of the linearized Benjamin-Bona-Mahony equation,” SIAM Journal on Control and Optimization, vol. 39, no. 6, pp. 1677–1696, 2001.
- Q. Tao, H. Gao, and B. Zhang, “Approximate controllability of a parabolic equation with memory,” Nonlinear Analysis. Hybrid Systems, vol. 6, no. 2, pp. 839–845, 2012.
- L. Rosier and P. Rouchon, “On the controllability of a wave equation with structural damping,” International Journal of Tomography & Statistics, vol. 5, pp. 79–84, 2007.
- P.-F. Yao, “On the observability inequalities for exact controllability of wave equations with variable coefficients,” SIAM Journal on Control and Optimization, vol. 37, no. 5, pp. 1568–1599, 1999.