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Uniform attractor for non-autonomous nonlinear Schrödinger equation
1. | Universite de Picardie Jules Verne, LAMFA UMR 7352, 33 rue Saint-Leu, 80039 Amiens cedex |
2. | Département de Mathématiques, Faculté des Sciences de Monastir, Av. de l'environement, 5000 Monastir, Tunisia |
References:
[1] |
N. Akroune, Regularity of the attractor for a weakly damped nonlinear Schrödinger equation on $\mathbb R$, Appl. Math. Lett, 12 (1999), 45-48.
doi: doi:10.1016/S0893-9659(98)00170-0. |
[2] |
A. Babin and M. Vishik, "Attractors of Evolution Equations," Nauka, Moscow 1989; English transl. Stud. Math. Appl., vol 25, North Holland, Amsterdam 1992. |
[3] |
J. Ball, Global attractors for damped semilinear wave equations, partial differential equations and applications, Discrete Contin. Dyn. Syst., 10 (2004), 31-52.
doi: doi:10.3934/dcds.2004.10.31. |
[4] |
T. Cazenave, "Semilinear Schrödinger Equations," vol 10, Courant Lectures Notes in Mathematics, NYU Courant Institute of Mathematical Sciences, New York, 2003. |
[5] |
V. V. Chepyzhov and M. I. Vishik, Attractor of non-autonomous dynamical systems and their dimension, J. Math. Pures Appl., 73 (1994), 279-333. |
[6] |
J.-M. Ghidaglia, Finite dimensional behavior for the weakly damped driven Schrödinger equations, Ann. Inst. Henri Poincaré, 5 (1988), 365-405. |
[7] |
O. Goubet, Regularity of the attractor for the weakly damped nonlinear Schrödinger equations, Applicable Anal., 60 (1996), 99-119. |
[8] |
P. Lauren\c cot, Long-time behavior for weakly damped driven nonlinear Schrödinger equation in $\mathbb R^N, N\leq 3$, No DEA, 2 (1995), 357-369.
doi: doi:10.1007/BF01261181. |
[9] |
A. Miranville and S. Zelik, "Attractors For Dissipative Partial Differential Equations In Bounded And Unbounded Domains," Handbook of Differential Equations: Evolutionary Equations, Vol. 4 (2008) 103-200. |
[10] |
I. Moise, R. Rosa and X. Wang, Attractors For noncompact nonautonomous systems via energy equations, Disrete Contin. Dyn. Syst., 10 (2004), 473-496.
doi: doi:10.3934/dcds.2004.10.473. |
[11] | |
[12] |
G. Raugel, "Global Attractor in Partial Differential Equations. Handbook of Dynamical Systems," Vol. 2, 885-982, North-Holland, Amsterdam, 2002. |
[13] |
R. Rosa, The global attractor of a weakly damped, forced Korteweg-De Vries equation in $H^1(R)$, VI workshop on partial differential equations, Part II (Rio de Janeiro, 1999), Mat. Contemp., 19 (2000), 129-152. |
[14] |
C. Sulem and P. L Sulem, "The Nonlinear Schröinger Equation. Self-focusing and Wave Collapse," Applied Mathematical Sciences, 139. Springer-Verlag, New York, 1999. |
[15] |
R. Temam, "Infinite Dimentional Dynamical Systems in Mecanics And physics," 2nd Edition, Springer-Verlag, 1997. |
[16] |
X. Wang, An energy equation for the weakly damped driven nonlinear Schrödinger equations and its applications, Physica D, 88 (1995), 167-175.
doi: doi:10.1016/0167-2789(95)00196-B. |
show all references
References:
[1] |
N. Akroune, Regularity of the attractor for a weakly damped nonlinear Schrödinger equation on $\mathbb R$, Appl. Math. Lett, 12 (1999), 45-48.
doi: doi:10.1016/S0893-9659(98)00170-0. |
[2] |
A. Babin and M. Vishik, "Attractors of Evolution Equations," Nauka, Moscow 1989; English transl. Stud. Math. Appl., vol 25, North Holland, Amsterdam 1992. |
[3] |
J. Ball, Global attractors for damped semilinear wave equations, partial differential equations and applications, Discrete Contin. Dyn. Syst., 10 (2004), 31-52.
doi: doi:10.3934/dcds.2004.10.31. |
[4] |
T. Cazenave, "Semilinear Schrödinger Equations," vol 10, Courant Lectures Notes in Mathematics, NYU Courant Institute of Mathematical Sciences, New York, 2003. |
[5] |
V. V. Chepyzhov and M. I. Vishik, Attractor of non-autonomous dynamical systems and their dimension, J. Math. Pures Appl., 73 (1994), 279-333. |
[6] |
J.-M. Ghidaglia, Finite dimensional behavior for the weakly damped driven Schrödinger equations, Ann. Inst. Henri Poincaré, 5 (1988), 365-405. |
[7] |
O. Goubet, Regularity of the attractor for the weakly damped nonlinear Schrödinger equations, Applicable Anal., 60 (1996), 99-119. |
[8] |
P. Lauren\c cot, Long-time behavior for weakly damped driven nonlinear Schrödinger equation in $\mathbb R^N, N\leq 3$, No DEA, 2 (1995), 357-369.
doi: doi:10.1007/BF01261181. |
[9] |
A. Miranville and S. Zelik, "Attractors For Dissipative Partial Differential Equations In Bounded And Unbounded Domains," Handbook of Differential Equations: Evolutionary Equations, Vol. 4 (2008) 103-200. |
[10] |
I. Moise, R. Rosa and X. Wang, Attractors For noncompact nonautonomous systems via energy equations, Disrete Contin. Dyn. Syst., 10 (2004), 473-496.
doi: doi:10.3934/dcds.2004.10.473. |
[11] | |
[12] |
G. Raugel, "Global Attractor in Partial Differential Equations. Handbook of Dynamical Systems," Vol. 2, 885-982, North-Holland, Amsterdam, 2002. |
[13] |
R. Rosa, The global attractor of a weakly damped, forced Korteweg-De Vries equation in $H^1(R)$, VI workshop on partial differential equations, Part II (Rio de Janeiro, 1999), Mat. Contemp., 19 (2000), 129-152. |
[14] |
C. Sulem and P. L Sulem, "The Nonlinear Schröinger Equation. Self-focusing and Wave Collapse," Applied Mathematical Sciences, 139. Springer-Verlag, New York, 1999. |
[15] |
R. Temam, "Infinite Dimentional Dynamical Systems in Mecanics And physics," 2nd Edition, Springer-Verlag, 1997. |
[16] |
X. Wang, An energy equation for the weakly damped driven nonlinear Schrödinger equations and its applications, Physica D, 88 (1995), 167-175.
doi: doi:10.1016/0167-2789(95)00196-B. |
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