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Applicable Analysis
An International Journal
Volume 94, 2015 - Issue 11
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Articles

Decay of solutions and structural stability for the coupled Kuramoto-Sivashinsky–Ginzburg-Landau equations

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Pages 2342-2354 | Received 20 Sep 2014, Accepted 03 Oct 2014, Published online: 08 Dec 2014

References

  • Golovin AA, Nepomnyashichy AA, Pismen LM. Interaction between short-scale Marangoni convection and long-scale deformational instability. Phys. Fluids. 1994;6:34–48.
  • Kazhdan D, Shtilman L, Golovin AA, Pismen LM. Nonlinear waves and turbulence in Marangoni convection. Phys. Fluids. 1995;7:2679–2685.
  • Duan J, Bu C, Gao H, Taboada M. On coupled Kuramoto–Sivashinski and Ginzburg–Landau type model for the Marangony convection. J. Math. Phys. 1997;38:2465–2474.
  • Gao H, Duan J. A remark on the coupled Kuramoto–Sivashinsky and Ginzburg–Landau equations. Comm. Appl. Nonlinear Anal. 1998;5:83–90.
  • Kalantarov VK. Global solution of coupled Kuramoto–Sivashinsky and Ginzburg–Landau equations. Nonlinear problems in mathematical physics and related topics, II. Vol. 2, International Mathematical Series. New York (NY): Kluwer/Plenum; 2002. p. 213–227.
  • Ames KA. Continuous dependence on modelling and non-existence results for a Ginzburg–Landau equation. Math. Methods Appl. Sci. 2000;23:1537–1550.
  • Celebi AO, Ugurlu D, Kalantarov VK. Continuous dependence for the convective Brinkman–Forchheimer equations. Applicable Aanal. 2005;84:877–888.
  • Celebi AO, Ugurlu D, Kalantarov VK. Structural stability for the double diffusive convective Brinkman equations. Applicable Anal. 2008;87:933–942.
  • Liu Y. Convergence and continuous dependence for the Brinkman–Forchheimer equations. Math. Comput. Modelling. 2009;49:1401–1415.
  • Payne LE, Straughan B. Unconditional nonlinear stability in temperature – dependent viscosity flow in a porous medium. Stud. Appl. Math. 2000;105:59–81.
  • Scott NL, Straughan B. Continuous dependence on the reaction terms in porous convection with surface reactions. Quart. Appl. Math. 2013;71:501–508.
  • Ames KA, Straughan B. Non-standard and improperly posed problems. San Diego (CA): Academic Press; 1997.
  • Straughan B. Stability and wave motion in porous media. Vol. 165, Applied Mathematical Sciences. New York (NY): Springer; 2008. xiv+437 pp.

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