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Global attractors for strongly damped wave equations with subcritical-critical nonlinearities
1. | Dipartimento di Matematica "Francesco Brioschi", Politecnico di Milano, Via Bonardi 9, Milano 20133, Italy |
References:
[1] |
A. V. Babin and M. I. Vishik, "Attractors of Evolution Equations," North-Holland, Amsterdam, 1992. |
[2] |
A. N. Carvalho and J. W. Cholewa, Attractors for strongly damped wave equations with critical nonlinearities, Pacific J. Math., 207 (2002), 287-310.
doi: 10.2140/pjm.2002.207.287. |
[3] |
I. Chueshov and I. Lasiecka, Long-time behavior of second order evolution equations with nonlinear damping, Mem. Amer. Math. Soc., 195 (2008), viii+183 pp. |
[4] |
M. Conti and V. Pata, On the regularity of global attractors, Discrete Cont. Dyn. Sys., 25 (2009), 1209-1217.
doi: 10.3934/dcds.2009.25.1209. |
[5] |
F. Dell'Oro and V. Pata, Long-term analysis of strongly damped nonlinear wave equations, Nonlinearity, 24 (2011), 3413-3435.
doi: 10.1088/0951-7715/24/12/006. |
[6] |
F. Dell'Oro and V. Pata, Strongly damped wave equations with critical nonlinearities, Nonlinear Anal., 75 (2012), 5723-5735. |
[7] |
A. E. Green and P. M. Naghdi, On undamped heat waves in an elastic solid, J. Thermal Stresses, 15 (1992), 253-264.
doi: 10.1080/01495739208946136. |
[8] |
A. E. Green and P. M. Naghdi, Thermoelasticity without energy dissipation, J. Elasticity, 31 (1993), 189-208.
doi: 10.1007/BF00044969. |
[9] |
A. E. Green and P. M. Naghdi, A unified procedure for construction of theories of deformable media. I. Classical continuum physics, Proc. Roy. Soc. London A, 448 (1995), 335-356.
doi: 10.1098/rspa.1995.0020. |
[10] |
A. E. Green and P. M. Naghdi, A unified procedure for construction of theories of deformable media. II. Generalized continua, Proc. Roy. Soc. London A, 448 (1995), 357-377.
doi: 10.1098/rspa.1995.0021. |
[11] |
A. E. Green and P. M. Naghdi, A unified procedure for construction of theories of deformable media. III. Mixtures of interacting continua, Proc. Roy. Soc. London A, 448 (1995), 379-388.
doi: 10.1098/rspa.1995.0022. |
[12] |
J. K. Hale, "Asymptotic Behavior of Dissipative Systems," Amer. Math. Soc., Providence, 1988. |
[13] |
A. Haraux, "Systèmes Dynamiques Dissipatifs et Applications," Masson, Paris, 1991. |
[14] |
A. Kh. Khanmamedov, On the existence of a global attractor for the wave equation with nonlinear strong damping perturbed by nonmonotone term, Nonlinear Anal., 69 (2008), 3372-3385.
doi: 10.1016/j.na.2007.09.028. |
[15] |
V. Pata, Uniform estimates of Gronwall type, J. Math. Anal. Appl., 373 (2011), 264-270.
doi: 10.1016/j.jmaa.2010.07.006. |
[16] |
V. Pata and M. Squassina, On the strongly damped wave equation, Comm. Math. Phys., 253 (2005), 511-533.
doi: 10.1007/s00220-004-1233-1. |
[17] |
V. Pata and S. Zelik, A result on the existence of global attractors for semigroups of closed operators, Commun. Pure Appl. Anal., 6 (2007), 481-486.
doi: 10.3934/cpaa.2007.6.481. |
[18] |
V. Pata and S. Zelik, Smooth attractors for strongly damped wave equations, Nonlinearity, 19 (2006), 1495-1506.
doi: 10.1088/0951-7715/19/7/001. |
[19] |
R. Temam, "Infinite-Dimensional Dynamical Systems in Mechanics and Physics," Springer, New York, 1997. |
show all references
References:
[1] |
A. V. Babin and M. I. Vishik, "Attractors of Evolution Equations," North-Holland, Amsterdam, 1992. |
[2] |
A. N. Carvalho and J. W. Cholewa, Attractors for strongly damped wave equations with critical nonlinearities, Pacific J. Math., 207 (2002), 287-310.
doi: 10.2140/pjm.2002.207.287. |
[3] |
I. Chueshov and I. Lasiecka, Long-time behavior of second order evolution equations with nonlinear damping, Mem. Amer. Math. Soc., 195 (2008), viii+183 pp. |
[4] |
M. Conti and V. Pata, On the regularity of global attractors, Discrete Cont. Dyn. Sys., 25 (2009), 1209-1217.
doi: 10.3934/dcds.2009.25.1209. |
[5] |
F. Dell'Oro and V. Pata, Long-term analysis of strongly damped nonlinear wave equations, Nonlinearity, 24 (2011), 3413-3435.
doi: 10.1088/0951-7715/24/12/006. |
[6] |
F. Dell'Oro and V. Pata, Strongly damped wave equations with critical nonlinearities, Nonlinear Anal., 75 (2012), 5723-5735. |
[7] |
A. E. Green and P. M. Naghdi, On undamped heat waves in an elastic solid, J. Thermal Stresses, 15 (1992), 253-264.
doi: 10.1080/01495739208946136. |
[8] |
A. E. Green and P. M. Naghdi, Thermoelasticity without energy dissipation, J. Elasticity, 31 (1993), 189-208.
doi: 10.1007/BF00044969. |
[9] |
A. E. Green and P. M. Naghdi, A unified procedure for construction of theories of deformable media. I. Classical continuum physics, Proc. Roy. Soc. London A, 448 (1995), 335-356.
doi: 10.1098/rspa.1995.0020. |
[10] |
A. E. Green and P. M. Naghdi, A unified procedure for construction of theories of deformable media. II. Generalized continua, Proc. Roy. Soc. London A, 448 (1995), 357-377.
doi: 10.1098/rspa.1995.0021. |
[11] |
A. E. Green and P. M. Naghdi, A unified procedure for construction of theories of deformable media. III. Mixtures of interacting continua, Proc. Roy. Soc. London A, 448 (1995), 379-388.
doi: 10.1098/rspa.1995.0022. |
[12] |
J. K. Hale, "Asymptotic Behavior of Dissipative Systems," Amer. Math. Soc., Providence, 1988. |
[13] |
A. Haraux, "Systèmes Dynamiques Dissipatifs et Applications," Masson, Paris, 1991. |
[14] |
A. Kh. Khanmamedov, On the existence of a global attractor for the wave equation with nonlinear strong damping perturbed by nonmonotone term, Nonlinear Anal., 69 (2008), 3372-3385.
doi: 10.1016/j.na.2007.09.028. |
[15] |
V. Pata, Uniform estimates of Gronwall type, J. Math. Anal. Appl., 373 (2011), 264-270.
doi: 10.1016/j.jmaa.2010.07.006. |
[16] |
V. Pata and M. Squassina, On the strongly damped wave equation, Comm. Math. Phys., 253 (2005), 511-533.
doi: 10.1007/s00220-004-1233-1. |
[17] |
V. Pata and S. Zelik, A result on the existence of global attractors for semigroups of closed operators, Commun. Pure Appl. Anal., 6 (2007), 481-486.
doi: 10.3934/cpaa.2007.6.481. |
[18] |
V. Pata and S. Zelik, Smooth attractors for strongly damped wave equations, Nonlinearity, 19 (2006), 1495-1506.
doi: 10.1088/0951-7715/19/7/001. |
[19] |
R. Temam, "Infinite-Dimensional Dynamical Systems in Mechanics and Physics," Springer, New York, 1997. |
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