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Favard theory and fredholm alternative for disconjugate recurrent second order equations
Regularity of the global attractor for a nonlinear Schrödinger equation with a point defect
Unité de Recherche Multifractales et Ondelettes, Faculté des Sciences de Monastir, Université de Monastir, Av. de l'environnement, 5000 Monastir, Tunisie |
We consider a nonlinear Schrödinger equation with a delta-function impurity at the origin of the space domain. We study the asymptotic behavior of the solutions with the theory of infinite dynamical system. We first prove the existence of a global attractor in $H^1_0(-1, 1)$. We also establish that this global attractor is a compact subset of $H^{\frac{3}{2}-\epsilon}(-1, 1)$.
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X. Wang,
An energy equation for the weakly damped driven nonlinear Schrödinger equations and its applications, Physica D, 88 (1995), 167-175.
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show all references
References:
| [1] |
J. Ball,
Global attractors for damped semilinear wave equations, Partial differential equations and applications, Discrete Contin. Dyn. Syst., 10 (2004), 31-52.
doi: 10.3934/dcds.2004.10.31. |
| [2] |
T. Cazenave, Semilinear Schrödinger Equations, vol 10, Courant Lectures Notes in Mathematics, NYU Courant Institute of Mathematical Sciences, New York, 2003.
doi: 10.1090/cln/010. |
| [3] |
J.-M. Ghidaglia,
Finite dimensional behavior for the weakly damped driven Schrödinger equations, Ann. Inst. Henri Poincaré, 5 (1988), 365-405.
|
| [4] |
O. Goubet,
Regularity of the attractor for the weakly damped nonlinear Schrödinger equations, Applicable Anal., 60 (1996), 99-119.
doi: 10.1080/00036819608840420. |
| [5] |
I. Moise, R. Rosa and X. Wang,
Attractors for a non-compact semi-groups via energy equations, Nonlinearity, 11 (1998), 1369-1393.
doi: 10.1088/0951-7715/11/5/012. |
| [6] |
C. Sulem and P. L Sulem, The Nonlinear Schrödinger Equation. Self-focusing and Wave Collapse, Applied Mathematical Sciences, 139. Springer-Verlag, New York, 1999. |
| [7] |
X. Wang,
An energy equation for the weakly damped driven nonlinear Schrödinger equations and its applications, Physica D, 88 (1995), 167-175.
doi: 10.1016/0167-2789(95)00196-B. |
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