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Dynamical Systems
An International Journal
Volume 38, 2023 - Issue 1
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Research Article

Global attractor for a degenerate Klein–Gordon–Schrödinger-type system

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Pages 121-139 | Received 23 Aug 2022, Accepted 03 Nov 2022, Published online: 17 Nov 2022

References

  • Ball J.M., Global attractors for damped semilinear wave equations, Discrete Contin. Dyn. Syst. 10(1–2) (2004), pp. 31–52.
  • Cardiroli P. and Musina R., On a variational degenerate elliptic problem, NoDEA Nonlinear Differ. Equ. Appl. 7 (2000), pp. 187–199.
  • Dautray R. and Lions J.L., Mathematical Analysis and Numerical Methods for Science and Technology, Vol. I, Physical origins and classical methods, Springer – Verlag, Berlin, 1985.
  • Flahaut I., Attractors for the dissipative Zakharov system, Nonlinear Anal. Theor. Methods Appl. 16(7/8) (1991), pp. 599–633.
  • Ginibre J. and Velo G., The Cauchy problem in local spaces for the complex Ginzburg–Landau equation II: contraction methods, Phys. D 95 (1996), pp. 191–288.
  • Ginibre J. and Velo G., The Cauchy problem in local spaces for the complex Ginzburg–Landau equation II: contraction methods, Commun. Math. Phys. 187 (1997), pp. 45–79.
  • Ghidaglia J.M. and Heron B., Dimension of the attractors associated to the Ginzburg–Landau equation, Phys. D 28 (1987), pp. 282–304.
  • Guo B. and Li Y., Attractors for Klein–Gordon–Schrödinger equations in IR3, J. Differ. Equ. 136 (1997), pp. 356–377.
  • Karachalios N., Stavrakakis N.M., and Xanthopoulos P., Parametric exponential energy decay for dissipative electron-Ion plasma waves, Z. Für Angew. Math. Phys. 56(2) (2005),pp. 218–238.
  • Karachalios N. and Zographopoulos N., Convergence towards attractors for a degenerate Ginzburg–Landau equation, Z. Für Angew. Math. Phys. 56(2) (2005), pp. 11–30.
  • Levermore C.D. and Oliver M., The complex Ginzburg–Landau equation as a model problem, Lect. Appl. Math. 31 (1996), pp. 141–190.
  • Lu K. and Wang B., Global attractors for the Klein–Gordon–Schrödinger equation in unbounded domains, J. Differ. Equ. 170 (2001), pp. 281–316.
  • Mielke A., Attractors for modulation equations on unbounded domains: existence and comparison, Nonlinearity 8 (1995), pp. 743–768.
  • Mielke A., The complex Ginzburg–Landau equation on large and unbounded domains: sharp bounds and attractors, Nonlinearity 10 (1997), pp. 199–222.
  • Poulou M.N. and Stavrakakis N.M., Global Attractor for a Klein–Gordon–Schrödinger Type System, Discrete Continuous Dynamical Systems, Supplements Vol. 2007, 2007, pp. 844–854
  • Poulou M.N. and Stavrakakis N.M., Finite dimensionality of the attractor of a system of Klein–Gordon–Schrödinger, Discrete Contin. Dyn. Syst. Ser. S 2(1) (2009), pp. 149–161.
  • Xanthopoulos P. and Zouraris G., A linearly implicit finite difference method for a Klein–Gordon–Schrödinger system modeling electron-ion plasma waves, Discrete Contin. Dyn. Syst. Ser. B 10(1) (2008), pp. 239–263.

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