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Attractors for weakly damped beam equations with $p$-Laplacian
1. | Instituto de Ci^encias Matemáticas e de Computação, Universidade de São Paulo, 13566-590, São Carlos, SP, Brazil |
2. | Departamento de Ciências, Campus Regional de Goioerê, Universidade Estadual de Maringá, 87360-000, Goioerê, PR, Brazil |
References:
[1] |
L. An and A. Peirce, A weakly nonlinear analysis of elasto-plastic-microstructure models,, SIAM J. Appl. Math., 55 (1995), 136.
|
[2] |
D. Andrade, M. A. Jorge Silva and T. F. Ma, Exponential stability for a plate equation with $p$-Laplacian and memory terms,, Math. Meth. Appl. Sci., 35 (2012), 417.
|
[3] |
A. V. Babin and M. I. Vishik, "Attractors of Evolution Equations,'', Studies in Mathematics and its Application 25, (1992).
|
[4] |
I. Chueshov and I. Lasiecka, "Von Karman Evolution Equations, Well-Posedness and Long-Time Dynamics,'', Springer Monographs in Mathematics, (2010).
|
[5] |
I. Chueshov and I. Lasiecka, Existence, uniqueness of weakly solutions and global attractors for a class of nonlinear 2D Kirchhoff-Boussinesq models,, Discrete Contin. Dyn. Syst., 15 (2006), 777.
|
[6] |
I. Chueshov and I. Lasiecka, On global attractor for 2D Kirchhoff-Boussinesq model with supercritical nonlinearity,, Comm. Partial Differential Equations, 36 (2011), 67.
|
[7] |
J. K. Hale, "Asymptotic Behavior of Dissipative Systems,'', Mathematical Surveys and Monographs, (1988).
|
[8] |
J. U. Kim, A boundary thin obstacle problem for a wave equation,, Comm. Partial Differential Equations, 14 (1989), 1011.
|
[9] |
O. Ladyzhenskaya, "Attractors for Semigroups and Evolution Equations,'', Cambridge University Press, (1991).
|
[10] |
J. L. Lions, "Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires,'', Dunod Gauthier-Villars, (1969).
|
[11] |
R. Temam, "Infinite-Dimensional Dynamical Systems in Mechanics and Physics,'', Applied Mathematical Sciences 68, (1988).
|
[12] |
Yang Zhijian, Global existence, asymptotic behavior and blowup of solutions for a class of nonlinear wave equations with dissipative term,, J. Differential Equations, 187 (2003), 520.
|
[13] |
Yang Zhijian, Longtime behavior for a nonlinear wave equation arising in elasto-plastic flow,, Math. Meth. Appl. Sci., 32 (2009), 1082.
|
[14] |
Yang Zhijian, Finite-dimensional attractors for the Kirchhoff models,, J. Math. Phys., 51 (2010).
|
[15] |
Yang Zhijian and Jin Baoxia, Global attractor for a class of Kirchhoff models,, J. Math. Phys., 50 (2009).
|
show all references
References:
[1] |
L. An and A. Peirce, A weakly nonlinear analysis of elasto-plastic-microstructure models,, SIAM J. Appl. Math., 55 (1995), 136.
|
[2] |
D. Andrade, M. A. Jorge Silva and T. F. Ma, Exponential stability for a plate equation with $p$-Laplacian and memory terms,, Math. Meth. Appl. Sci., 35 (2012), 417.
|
[3] |
A. V. Babin and M. I. Vishik, "Attractors of Evolution Equations,'', Studies in Mathematics and its Application 25, (1992).
|
[4] |
I. Chueshov and I. Lasiecka, "Von Karman Evolution Equations, Well-Posedness and Long-Time Dynamics,'', Springer Monographs in Mathematics, (2010).
|
[5] |
I. Chueshov and I. Lasiecka, Existence, uniqueness of weakly solutions and global attractors for a class of nonlinear 2D Kirchhoff-Boussinesq models,, Discrete Contin. Dyn. Syst., 15 (2006), 777.
|
[6] |
I. Chueshov and I. Lasiecka, On global attractor for 2D Kirchhoff-Boussinesq model with supercritical nonlinearity,, Comm. Partial Differential Equations, 36 (2011), 67.
|
[7] |
J. K. Hale, "Asymptotic Behavior of Dissipative Systems,'', Mathematical Surveys and Monographs, (1988).
|
[8] |
J. U. Kim, A boundary thin obstacle problem for a wave equation,, Comm. Partial Differential Equations, 14 (1989), 1011.
|
[9] |
O. Ladyzhenskaya, "Attractors for Semigroups and Evolution Equations,'', Cambridge University Press, (1991).
|
[10] |
J. L. Lions, "Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires,'', Dunod Gauthier-Villars, (1969).
|
[11] |
R. Temam, "Infinite-Dimensional Dynamical Systems in Mechanics and Physics,'', Applied Mathematical Sciences 68, (1988).
|
[12] |
Yang Zhijian, Global existence, asymptotic behavior and blowup of solutions for a class of nonlinear wave equations with dissipative term,, J. Differential Equations, 187 (2003), 520.
|
[13] |
Yang Zhijian, Longtime behavior for a nonlinear wave equation arising in elasto-plastic flow,, Math. Meth. Appl. Sci., 32 (2009), 1082.
|
[14] |
Yang Zhijian, Finite-dimensional attractors for the Kirchhoff models,, J. Math. Phys., 51 (2010).
|
[15] |
Yang Zhijian and Jin Baoxia, Global attractor for a class of Kirchhoff models,, J. Math. Phys., 50 (2009).
|
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