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Reaction-diffusion equations with a switched--off reaction zone
Eliminating flutter for clamped von Karman plates immersed in subsonic flows
1. | University of Memphis, Department of Mathematical Sciences, 373 Dunn Hall, Memphis, TN 38152 |
2. | Oregon State University, Department of Mathematics, 368 Kidder Hall, Corvallis, OR 97330 |
References:
[1] |
A. Babin and M. Vishik, Attractors of Evolution Equations,, North-Holland, (1992).
|
[2] |
A. V. Balakrishnan, Aeroelasticity-Continuum Theory,, Springer-Verlag, (2012).
doi: 10.1007/978-1-4614-3609-6. |
[3] |
J. M. Ball, Global attractors for damped semilinear wave equations,, \emph{Discrete Contin. Dyn. Syst.}, 10 (2004), 31.
doi: 10.3934/dcds.2004.10.31. |
[4] |
R. Bisplinghoff and H. Ashley, Principles of Aeroelasticity,, Wiley, (1962).
|
[5] |
J. Bergh and J. Löfström, Interpolation Spaces. An Introduction,, Springer-Verlag, (1976).
|
[6] |
V. V. Bolotin, Nonconservative Problems of Elastic Stability,, Pergamon Press, (1963). Google Scholar |
[7] |
A. Boutet de Monvel and I. Chueshov, The problem of interaction of von Karman plate with subsonic flow gas,, \emph{Math. Methods in Appl. Sc.}, 22 (1999), 801.
doi: 10.1002/(SICI)1099-1476(19990710)22:10<801::AID-MMA61>3.0.CO;2-T. |
[8] |
L. Boutet de Monvel and I. Chueshov, Non-linear oscillations of a plate in a flow of gas, C.R., \emph{Acad. Sci. Paris, 322 (1996), 1001.
|
[9] |
L. Boutet de Monvel and I. Chueshov, Oscillation of von Karman's plate in a potential flow of gas,, \emph{Izvestiya RAN: Ser. Mat.}, 63 (1999), 219.
doi: 10.1070/im1999v063n02ABEH000237. |
[10] |
L. Boutet de Monvel, I. Chueshov and A. Rezounenko, Long-time behaviour of strong solutions of retarded nonlinear PDEs,, \emph{Comm. PDEs}, 22 (1997), 1453.
doi: 10.1080/03605309708821307. |
[11] |
I. Chueshov, On a certain system of equations with delay, occurring in aeroelasticity,, \emph{Teor. Funktsii Funktsional. Anal. i Prilozhen}, 54 (1990), 123.
doi: 10.1007/BF01097291. |
[12] |
I. Chueshov, Dynamics of von Karman plate in a potential flow of gas: rigorous results and unsolved problems,, \emph{Proceedings of the 16th IMACS World Congress}, (2000), 1. Google Scholar |
[13] |
I. Chueshov and I. Lasiecka, Long-time Behavior of Second-order Evolutions with Nonlinear Damping,, Memoires of AMS, (2008).
doi: 10.1090/memo/0912. |
[14] |
I. Chueshov and I. Lasiecka, Von Karman Evolution Equations, Well-posedness and Long-Time Behavior,, Monographs, (2010).
doi: 10.1007/978-0-387-87712-9. |
[15] |
I. Chueshov and I. Lasiecka, Generation of a semigroup and hidden regularity in nonlinear subsonic flow-structure interactions with absorbing boundary conditions,, \emph{Jour. Abstr. Differ. Equ. Appl.}, 3 (2012), 1.
|
[16] |
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,, arXiv:1208.5245, (2012). Google Scholar |
[17] |
I. Chueshov, I. Lasiecka and J. T. Webster, Evolution semigroups for supersonic flow-plate interactions,, \emph{J. of Diff. Eqs.}, 254 (2013), 1741.
doi: 10.1016/j.jde.2012.11.009. |
[18] |
I. Chueshov, I. Lasiecka and J. T. Webster, Flow-plate interactions: Well-posedness and long-time behavior,, \emph{Discrete Contin. Dyn. Syst. Ser. S, 7 (2014). Google Scholar |
[19] |
P. Ciarlet and P. Rabier, Les Equations de Von Karman,, Springer, (1980).
|
[20] |
C. M. Dafermos and M. Slemrod, Asymptotic behavior of nonlinear contraction semigroups,, \emph{J. Func. Anal}, 13 (1973), 97.
|
[21] |
E. Dowell, Nonlinear Oscillations of a Fluttering Plate, I and II,, \emph{AIAA J.}, 4 (1966), 1267. Google Scholar |
[22] |
E. Dowell, Panel flutter-A review of the aeroelastic stability of plates and shells,, \emph{AIAA Journal}, 8 (1970), 385. Google Scholar |
[23] |
E. Dowell, A Modern Course in Aeroelasticity,, Kluwer Academic Publishers, (2004).
|
[24] |
E. H. Dowell, Some recent advances in nonlinear aeroelasticity: fluid-structure interaction in the 21st century,, Proceedings of the 51st AIAA/ASME/ASCE/AHS/ASC Structures, (2010). Google Scholar |
[25] |
D. H. Hodges and G. A. Pierce, Introduction to Structural Dynamics and Aeroelasticity,, Cambridge Univ. Press, (2002). Google Scholar |
[26] |
E. A. Krasil'shchikova, The Thin Wing in a Compressible Flow,, Nauka, (1978). Google Scholar |
[27] |
H. Koch and I. Lasiecka, Hadamard well-posedness of weak solutions in nonlinear dynamic elasticity-full von Karman systems,, \emph{Prog. Nonlin. Differential Eqs. and Their App.}, 50 (2002), 197.
|
[28] |
J. Lagnese, Boundary Stabilization of Thin Plates,, SIAM, (1989).
doi: 10.1137/1.9781611970821. |
[29] |
P. D. Lax and R. S. Phillips, Scattering Theory,, Academic Press, (1967).
|
[30] |
I. Lasiecka and J. T. Webster, Generation of bounded semigroups in nonlinear flow-structure interactions with boundary damping,, \emph{Math. Methods in App. Sc.}, (2011). Google Scholar |
[31] |
J.-L. Lions and E. Magenes, Problmes aux limites non homognes et applications,, vol. 1, (1968).
|
[32] |
E. Livne, Future of Airplane Aeroelasticity,, \emph{J. of Aircraft}, 40 (2003), 1066. Google Scholar |
[33] |
Y. Lu, Uniform decay rates for the energy in nonlinear fluid structure interactions with monotone viscous damping,, \emph{Palestine J. Mathematics}, 2 (2013), 215.
|
[34] |
S. Miyatake, Mixed problem for hyperbolic equation of second order,, \emph{J. Math. Kyoto Univ.}, 13 (1973), 435.
|
[35] |
A. Miranville and S. Zelik, Attractors for Dissipative Partial Differential Equations in Bounded and Unbounded Domains,, Handboook of Differential Equations, (2008).
doi: 10.1016/S1874-5717(08)00003-0. |
[36] |
I. Ryzhkova, Stabilization of a von Karman plate in the presence of thermal effects in a subsonic potential flow of gas,, \emph{J. Math. Anal. and Appl.}, 294 (2004), 462.
doi: 10.1016/j.jmaa.2004.02.021. |
[37] |
I. Ryzhkova, Dynamics of a thermoelastic von Karman plate in a subsonic gas flow,, \emph{Zeitschrift Ang. Math. Phys.}, 58 (2007), 246.
doi: 10.1007/s00033-006-0080-7. |
[38] |
M. Slemrod, Weak asymptotic decay via a "relaxed invariance principle" for a wave equation with nonlinear, nonmonotone damping,, \emph{Proc. Royal Soc., 113 (1989), 87.
doi: 10.1017/S0308210500023970. |
[39] |
D. Tataru, On the regularity of boundary traces for the wave equation,, \emph{Ann. Scuola Normale. Sup. di Pisa.}, 26 (1998), 185.
|
[40] |
R. Temam, Infinite Dimensional Dynamical Systems in Mechanics and Physics,, Springer-Verlag, (1988).
doi: 10.1007/978-1-4684-0313-8. |
[41] |
J. T. Webster, Weak and strong solutions of a nonlinear subsonic flow-structure interaction: semigroup approach,, \emph{Nonlinear Analysis}, 74 (2011), 3123.
doi: 10.1016/j.na.2011.01.028. |
show all references
References:
[1] |
A. Babin and M. Vishik, Attractors of Evolution Equations,, North-Holland, (1992).
|
[2] |
A. V. Balakrishnan, Aeroelasticity-Continuum Theory,, Springer-Verlag, (2012).
doi: 10.1007/978-1-4614-3609-6. |
[3] |
J. M. Ball, Global attractors for damped semilinear wave equations,, \emph{Discrete Contin. Dyn. Syst.}, 10 (2004), 31.
doi: 10.3934/dcds.2004.10.31. |
[4] |
R. Bisplinghoff and H. Ashley, Principles of Aeroelasticity,, Wiley, (1962).
|
[5] |
J. Bergh and J. Löfström, Interpolation Spaces. An Introduction,, Springer-Verlag, (1976).
|
[6] |
V. V. Bolotin, Nonconservative Problems of Elastic Stability,, Pergamon Press, (1963). Google Scholar |
[7] |
A. Boutet de Monvel and I. Chueshov, The problem of interaction of von Karman plate with subsonic flow gas,, \emph{Math. Methods in Appl. Sc.}, 22 (1999), 801.
doi: 10.1002/(SICI)1099-1476(19990710)22:10<801::AID-MMA61>3.0.CO;2-T. |
[8] |
L. Boutet de Monvel and I. Chueshov, Non-linear oscillations of a plate in a flow of gas, C.R., \emph{Acad. Sci. Paris, 322 (1996), 1001.
|
[9] |
L. Boutet de Monvel and I. Chueshov, Oscillation of von Karman's plate in a potential flow of gas,, \emph{Izvestiya RAN: Ser. Mat.}, 63 (1999), 219.
doi: 10.1070/im1999v063n02ABEH000237. |
[10] |
L. Boutet de Monvel, I. Chueshov and A. Rezounenko, Long-time behaviour of strong solutions of retarded nonlinear PDEs,, \emph{Comm. PDEs}, 22 (1997), 1453.
doi: 10.1080/03605309708821307. |
[11] |
I. Chueshov, On a certain system of equations with delay, occurring in aeroelasticity,, \emph{Teor. Funktsii Funktsional. Anal. i Prilozhen}, 54 (1990), 123.
doi: 10.1007/BF01097291. |
[12] |
I. Chueshov, Dynamics of von Karman plate in a potential flow of gas: rigorous results and unsolved problems,, \emph{Proceedings of the 16th IMACS World Congress}, (2000), 1. Google Scholar |
[13] |
I. Chueshov and I. Lasiecka, Long-time Behavior of Second-order Evolutions with Nonlinear Damping,, Memoires of AMS, (2008).
doi: 10.1090/memo/0912. |
[14] |
I. Chueshov and I. Lasiecka, Von Karman Evolution Equations, Well-posedness and Long-Time Behavior,, Monographs, (2010).
doi: 10.1007/978-0-387-87712-9. |
[15] |
I. Chueshov and I. Lasiecka, Generation of a semigroup and hidden regularity in nonlinear subsonic flow-structure interactions with absorbing boundary conditions,, \emph{Jour. Abstr. Differ. Equ. Appl.}, 3 (2012), 1.
|
[16] |
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,, arXiv:1208.5245, (2012). Google Scholar |
[17] |
I. Chueshov, I. Lasiecka and J. T. Webster, Evolution semigroups for supersonic flow-plate interactions,, \emph{J. of Diff. Eqs.}, 254 (2013), 1741.
doi: 10.1016/j.jde.2012.11.009. |
[18] |
I. Chueshov, I. Lasiecka and J. T. Webster, Flow-plate interactions: Well-posedness and long-time behavior,, \emph{Discrete Contin. Dyn. Syst. Ser. S, 7 (2014). Google Scholar |
[19] |
P. Ciarlet and P. Rabier, Les Equations de Von Karman,, Springer, (1980).
|
[20] |
C. M. Dafermos and M. Slemrod, Asymptotic behavior of nonlinear contraction semigroups,, \emph{J. Func. Anal}, 13 (1973), 97.
|
[21] |
E. Dowell, Nonlinear Oscillations of a Fluttering Plate, I and II,, \emph{AIAA J.}, 4 (1966), 1267. Google Scholar |
[22] |
E. Dowell, Panel flutter-A review of the aeroelastic stability of plates and shells,, \emph{AIAA Journal}, 8 (1970), 385. Google Scholar |
[23] |
E. Dowell, A Modern Course in Aeroelasticity,, Kluwer Academic Publishers, (2004).
|
[24] |
E. H. Dowell, Some recent advances in nonlinear aeroelasticity: fluid-structure interaction in the 21st century,, Proceedings of the 51st AIAA/ASME/ASCE/AHS/ASC Structures, (2010). Google Scholar |
[25] |
D. H. Hodges and G. A. Pierce, Introduction to Structural Dynamics and Aeroelasticity,, Cambridge Univ. Press, (2002). Google Scholar |
[26] |
E. A. Krasil'shchikova, The Thin Wing in a Compressible Flow,, Nauka, (1978). Google Scholar |
[27] |
H. Koch and I. Lasiecka, Hadamard well-posedness of weak solutions in nonlinear dynamic elasticity-full von Karman systems,, \emph{Prog. Nonlin. Differential Eqs. and Their App.}, 50 (2002), 197.
|
[28] |
J. Lagnese, Boundary Stabilization of Thin Plates,, SIAM, (1989).
doi: 10.1137/1.9781611970821. |
[29] |
P. D. Lax and R. S. Phillips, Scattering Theory,, Academic Press, (1967).
|
[30] |
I. Lasiecka and J. T. Webster, Generation of bounded semigroups in nonlinear flow-structure interactions with boundary damping,, \emph{Math. Methods in App. Sc.}, (2011). Google Scholar |
[31] |
J.-L. Lions and E. Magenes, Problmes aux limites non homognes et applications,, vol. 1, (1968).
|
[32] |
E. Livne, Future of Airplane Aeroelasticity,, \emph{J. of Aircraft}, 40 (2003), 1066. Google Scholar |
[33] |
Y. Lu, Uniform decay rates for the energy in nonlinear fluid structure interactions with monotone viscous damping,, \emph{Palestine J. Mathematics}, 2 (2013), 215.
|
[34] |
S. Miyatake, Mixed problem for hyperbolic equation of second order,, \emph{J. Math. Kyoto Univ.}, 13 (1973), 435.
|
[35] |
A. Miranville and S. Zelik, Attractors for Dissipative Partial Differential Equations in Bounded and Unbounded Domains,, Handboook of Differential Equations, (2008).
doi: 10.1016/S1874-5717(08)00003-0. |
[36] |
I. Ryzhkova, Stabilization of a von Karman plate in the presence of thermal effects in a subsonic potential flow of gas,, \emph{J. Math. Anal. and Appl.}, 294 (2004), 462.
doi: 10.1016/j.jmaa.2004.02.021. |
[37] |
I. Ryzhkova, Dynamics of a thermoelastic von Karman plate in a subsonic gas flow,, \emph{Zeitschrift Ang. Math. Phys.}, 58 (2007), 246.
doi: 10.1007/s00033-006-0080-7. |
[38] |
M. Slemrod, Weak asymptotic decay via a "relaxed invariance principle" for a wave equation with nonlinear, nonmonotone damping,, \emph{Proc. Royal Soc., 113 (1989), 87.
doi: 10.1017/S0308210500023970. |
[39] |
D. Tataru, On the regularity of boundary traces for the wave equation,, \emph{Ann. Scuola Normale. Sup. di Pisa.}, 26 (1998), 185.
|
[40] |
R. Temam, Infinite Dimensional Dynamical Systems in Mechanics and Physics,, Springer-Verlag, (1988).
doi: 10.1007/978-1-4684-0313-8. |
[41] |
J. T. Webster, Weak and strong solutions of a nonlinear subsonic flow-structure interaction: semigroup approach,, \emph{Nonlinear Analysis}, 74 (2011), 3123.
doi: 10.1016/j.na.2011.01.028. |
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