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Remark on an elastic plate interacting with a gas in a semi-infinite tube: Periodic solutions
1. | Kharkiv Karazin National University, 4 Svobody sq., 61077 Kharkiv, Ukraine |
References:
[1] |
I. Chueshov, Introduction to the Theory of Infinite-Dimensional Dissipative Systems, Acta, Kharkov, 1999 (in Russian); English translation: Acta, Kharkov, 2002; see also http://www.emis.de/monographs/Chueshov/ |
[2] |
I. Chueshov, Dynamics of von Karman plate in a potential flow of gas: rigorous results and unsolved problems, Proceedings of the 16th IMACS World Congress, Lausanne (Switzerland), 2000, 1-6. |
[3] |
I. Chueshov, E. Dowell, I. Lasiecka and J. T. Webster, Von Karman plate in a gas flow: Recent results and conjectures, Appl. Math. Optim., 73 (2016), 475-500.
doi: 10.1007/s00245-016-9349-1. |
[4] |
I. Chueshov and I. Lasiecka, Existence, uniqueness of weak solutions and global attractors for a class of nonlinear 2D Kirchhoff-Boussinesq models, Discr. Cont. Dyn. Sys., 15 (2006), 777-809.
doi: 10.3934/dcds.2006.15.777. |
[5] |
I. Chueshov and I. Lasiecka, Von Karman Evolution Equations. Well-posedness and Long Time Behavior, Monographs, {Springer-Verlag}, 2010.
doi: 10.1007/978-0-387-87712-9. |
[6] |
I. Chueshov and I. Lasiecka, Generation of a semigroup and hidden regularity in nonlinear subsonic flow-structure interactions with absorbing boundary conditions. Jour. Abstr. Differ. Equ. Appl., 3 (2012), 1-27. |
[7] |
I. Chueshov, I. Lasiecka and J. T. Webster, Attractors for delayed, non-rotational von Karman plates with applications to flow-structure interactions without any damping, Comm. in PDE, 39 (2014), 1965-1997.
doi: 10.1080/03605302.2014.930484. |
[8] |
I. Chueshov, I. Lasiecka and J. T. Webster, Flow-plate interactions: Well-posedness and long-time behavior, Discrete Contin. Dyn. Syst. Ser. S, Special Volume: New Developments in Mathematical Theory of Fluid Mechanics, 7 (2014), 925-965.
doi: 10.3934/dcdss.2014.7.925. |
[9] |
I. Lasiecka, Mathematical Control Theory of Coupled PDE's, CMBS-NSF Lecture Notes, SIAM Publications, 2002.
doi: 10.1137/1.9780898717099. |
[10] |
I. Lasiecka and J. T. Webster, Eliminating flutter for clamped von Karman plates immersed in subsonic flows, Comm. Pure Appl. Math., 13 (2014), 1935-1969, Updated version (May, 2015): Arxiv:1409.3308v5.
doi: 10.3934/cpaa.2014.13.1935. |
[11] |
I. Lasiecka and J. T. Webster, Feedback stabilization of a fluttering panel in an inviscid subsonic potential flow, SIAM J. Math. Anal., 48 (2016), 1848-1891.
doi: 10.1137/15M1040529. |
[12] |
H. F. Walker, Some remarks on the local energy decay of solutions of the initial-boundary value problem for the wave equation in unbounded domains, J. Diff. Eqs., 23 (1977), 459-471.
doi: 10.1016/0022-0396(77)90123-1. |
show all references
References:
[1] |
I. Chueshov, Introduction to the Theory of Infinite-Dimensional Dissipative Systems, Acta, Kharkov, 1999 (in Russian); English translation: Acta, Kharkov, 2002; see also http://www.emis.de/monographs/Chueshov/ |
[2] |
I. Chueshov, Dynamics of von Karman plate in a potential flow of gas: rigorous results and unsolved problems, Proceedings of the 16th IMACS World Congress, Lausanne (Switzerland), 2000, 1-6. |
[3] |
I. Chueshov, E. Dowell, I. Lasiecka and J. T. Webster, Von Karman plate in a gas flow: Recent results and conjectures, Appl. Math. Optim., 73 (2016), 475-500.
doi: 10.1007/s00245-016-9349-1. |
[4] |
I. Chueshov and I. Lasiecka, Existence, uniqueness of weak solutions and global attractors for a class of nonlinear 2D Kirchhoff-Boussinesq models, Discr. Cont. Dyn. Sys., 15 (2006), 777-809.
doi: 10.3934/dcds.2006.15.777. |
[5] |
I. Chueshov and I. Lasiecka, Von Karman Evolution Equations. Well-posedness and Long Time Behavior, Monographs, {Springer-Verlag}, 2010.
doi: 10.1007/978-0-387-87712-9. |
[6] |
I. Chueshov and I. Lasiecka, Generation of a semigroup and hidden regularity in nonlinear subsonic flow-structure interactions with absorbing boundary conditions. Jour. Abstr. Differ. Equ. Appl., 3 (2012), 1-27. |
[7] |
I. Chueshov, I. Lasiecka and J. T. Webster, Attractors for delayed, non-rotational von Karman plates with applications to flow-structure interactions without any damping, Comm. in PDE, 39 (2014), 1965-1997.
doi: 10.1080/03605302.2014.930484. |
[8] |
I. Chueshov, I. Lasiecka and J. T. Webster, Flow-plate interactions: Well-posedness and long-time behavior, Discrete Contin. Dyn. Syst. Ser. S, Special Volume: New Developments in Mathematical Theory of Fluid Mechanics, 7 (2014), 925-965.
doi: 10.3934/dcdss.2014.7.925. |
[9] |
I. Lasiecka, Mathematical Control Theory of Coupled PDE's, CMBS-NSF Lecture Notes, SIAM Publications, 2002.
doi: 10.1137/1.9780898717099. |
[10] |
I. Lasiecka and J. T. Webster, Eliminating flutter for clamped von Karman plates immersed in subsonic flows, Comm. Pure Appl. Math., 13 (2014), 1935-1969, Updated version (May, 2015): Arxiv:1409.3308v5.
doi: 10.3934/cpaa.2014.13.1935. |
[11] |
I. Lasiecka and J. T. Webster, Feedback stabilization of a fluttering panel in an inviscid subsonic potential flow, SIAM J. Math. Anal., 48 (2016), 1848-1891.
doi: 10.1137/15M1040529. |
[12] |
H. F. Walker, Some remarks on the local energy decay of solutions of the initial-boundary value problem for the wave equation in unbounded domains, J. Diff. Eqs., 23 (1977), 459-471.
doi: 10.1016/0022-0396(77)90123-1. |
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