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Boundary stabilizability of the linearized viscous Saint-Venant system
1. | LAMSIN, Ecole Nationale d'Ingénieurs de Tunis, B.P. 37, 1002 Tunis Le Belvédère, Tunisia, Tunisia |
2. | Université de Technologie de Compiègne, BP 20529, 60205 Compiègne cedex, France |
3. | Université de Toulouse & CNRS, Institut de Mathématiques, UMR 5219, 31062 Toulouse Cedex 9 |
References:
[1] |
M. B. Abbott and A. W. Minns, "Computational Hydraulics," 2nd edition, Ashgate Publishing Company, Brookfield, USA, 1998. |
[2] |
S. N. Antontsev, A. V. Kazhikov and V. N. Monakhov, "Boundary Values Problems In Mechanics Of Nonhomogeneous Fluids," North-Holland, Amsterdam, 1990. |
[3] |
H. Arfaoui, "Contrôle et Stabilisation des Équations de Saint-Venant," Ph.D thesis, Université Tunis El Manar, Université Paul Sabatier Toulouse, 2006. |
[4] |
A. Bensoussan, G. Da Prato, M. C. Delfour and S. K. Mitter, "Representation and Control of Infinite Dimensional Systems," Vol. 2, Birkhäuser, 1993. |
[5] |
J. A. Cunge, F. M. Holly and Jr. A. Verwey, "Practical Aspects of Computational River Hydraulics," Pitman Advanced Publishing Program, Boston. London. Melbourne, 1980. |
[6] |
A. V. Fursikov, Stabilizability of quasilinear parabolic equation by by means of feedback boundary control, Sbornik Mathematics, 192 (2001), 593-639.
doi: 10.1070/SM2001v192n04ABEH000560. |
[7] |
A. V. Fursikov, Stabilizability of two-dimensional Navier-Stokes equations with help of boundary feedback control, J. Math. Fluid Mech., 3 (2001), 259-301.
doi: 10.1007/PL00000972. |
[8] |
A. V. Fursikov, Real Processes and Realizability of a Stabilization Method for Navier-Stokes Equations by Boundary Feedback Control, in "Nonlinear Problems in Mathematical Physics and Related Topics II, In Honor of Professor O. A. Ladyzhenskaya," Kluwer/Plenum Publishers, New-York, Boston, Dordrecht, London, Moscow, (2002), 137-177. |
[9] |
J.-F. Gerbeau and B. Perthame, Derivation of viscous Saint-Venant system for laminar shallow water; Numerical validation, Discrete Continuous Dynam. Systems - B, 1 (2001), 89-102. |
[10] |
J. de Halleux, C. Prieur, J.-M. Coron, B. d'Andréa-Novel and G. Bastin, Boundary feedback control in networks of open channels, Automatica, 39:8 (2003), 1365-1376.
doi: 10.1016/S0005-1098(03)00109-2. |
[11] |
Z. Huang, S. Jin, P. A. Markowich, C. Sparber and C. Zheng, A Time-Splitting spectral Scheme for the Dirac-Maxwell System, J. Comp. Physics, 208:2 (2005), 761-789.
doi: 10.1016/j.jcp.2005.02.026. |
[12] |
L. A. Khan and P. L.-F. Liu, Numerical analyses of operator-splitting algorithms for the two-dimensional advection-diffusion equation, Comput. Meth. Appl. Mech. Engng., 152 (1998), 337-359.
doi: 10.1016/S0045-7825(97)00127-8. |
[13] |
D. A. Lyn and P. Goodwin, Stability of a general Preissmann scheme, Journal of Hydraulic engineering, 113 (1987), 16-28.
doi: 10.1061/(ASCE)0733-9429(1987)113:1(16). |
[14] |
G. Mathieu, "Étude et Contrôle des Équations de la Théorie 'Shallow Water' en Dimension un," Ph.D thesis, Université Paul Sabatier Toulouse, 1998. |
[15] |
M. Renardy, Are viscoelastic flows under control or out of control?, Systems & Control Letters, 54 (2005), 1183-1193.
doi: 10.1016/j.sysconle.2005.04.006. |
[16] |
J. J. Stoker, "Water Waves, the Mathematical Theory with Applications," Pure and Applied Mathematics,, Vol. \textbf{IV}, IV ().
|
[17] |
D. H. Wagner, Equivalence of the Euler and Lagrangian equations of a gas dynamics for weak solutions, Journal of Differential Equations, 68 (1987), 118-136.
doi: 10.1016/0022-0396(87)90188-4. |
show all references
References:
[1] |
M. B. Abbott and A. W. Minns, "Computational Hydraulics," 2nd edition, Ashgate Publishing Company, Brookfield, USA, 1998. |
[2] |
S. N. Antontsev, A. V. Kazhikov and V. N. Monakhov, "Boundary Values Problems In Mechanics Of Nonhomogeneous Fluids," North-Holland, Amsterdam, 1990. |
[3] |
H. Arfaoui, "Contrôle et Stabilisation des Équations de Saint-Venant," Ph.D thesis, Université Tunis El Manar, Université Paul Sabatier Toulouse, 2006. |
[4] |
A. Bensoussan, G. Da Prato, M. C. Delfour and S. K. Mitter, "Representation and Control of Infinite Dimensional Systems," Vol. 2, Birkhäuser, 1993. |
[5] |
J. A. Cunge, F. M. Holly and Jr. A. Verwey, "Practical Aspects of Computational River Hydraulics," Pitman Advanced Publishing Program, Boston. London. Melbourne, 1980. |
[6] |
A. V. Fursikov, Stabilizability of quasilinear parabolic equation by by means of feedback boundary control, Sbornik Mathematics, 192 (2001), 593-639.
doi: 10.1070/SM2001v192n04ABEH000560. |
[7] |
A. V. Fursikov, Stabilizability of two-dimensional Navier-Stokes equations with help of boundary feedback control, J. Math. Fluid Mech., 3 (2001), 259-301.
doi: 10.1007/PL00000972. |
[8] |
A. V. Fursikov, Real Processes and Realizability of a Stabilization Method for Navier-Stokes Equations by Boundary Feedback Control, in "Nonlinear Problems in Mathematical Physics and Related Topics II, In Honor of Professor O. A. Ladyzhenskaya," Kluwer/Plenum Publishers, New-York, Boston, Dordrecht, London, Moscow, (2002), 137-177. |
[9] |
J.-F. Gerbeau and B. Perthame, Derivation of viscous Saint-Venant system for laminar shallow water; Numerical validation, Discrete Continuous Dynam. Systems - B, 1 (2001), 89-102. |
[10] |
J. de Halleux, C. Prieur, J.-M. Coron, B. d'Andréa-Novel and G. Bastin, Boundary feedback control in networks of open channels, Automatica, 39:8 (2003), 1365-1376.
doi: 10.1016/S0005-1098(03)00109-2. |
[11] |
Z. Huang, S. Jin, P. A. Markowich, C. Sparber and C. Zheng, A Time-Splitting spectral Scheme for the Dirac-Maxwell System, J. Comp. Physics, 208:2 (2005), 761-789.
doi: 10.1016/j.jcp.2005.02.026. |
[12] |
L. A. Khan and P. L.-F. Liu, Numerical analyses of operator-splitting algorithms for the two-dimensional advection-diffusion equation, Comput. Meth. Appl. Mech. Engng., 152 (1998), 337-359.
doi: 10.1016/S0045-7825(97)00127-8. |
[13] |
D. A. Lyn and P. Goodwin, Stability of a general Preissmann scheme, Journal of Hydraulic engineering, 113 (1987), 16-28.
doi: 10.1061/(ASCE)0733-9429(1987)113:1(16). |
[14] |
G. Mathieu, "Étude et Contrôle des Équations de la Théorie 'Shallow Water' en Dimension un," Ph.D thesis, Université Paul Sabatier Toulouse, 1998. |
[15] |
M. Renardy, Are viscoelastic flows under control or out of control?, Systems & Control Letters, 54 (2005), 1183-1193.
doi: 10.1016/j.sysconle.2005.04.006. |
[16] |
J. J. Stoker, "Water Waves, the Mathematical Theory with Applications," Pure and Applied Mathematics,, Vol. \textbf{IV}, IV ().
|
[17] |
D. H. Wagner, Equivalence of the Euler and Lagrangian equations of a gas dynamics for weak solutions, Journal of Differential Equations, 68 (1987), 118-136.
doi: 10.1016/0022-0396(87)90188-4. |
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