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

Abstract

We show that solutions of the initial boundary value problem for the coupled system of Kuramoto-Sivashinsky and Ginzburg-Landau (KS–GL) equations continuously depend on parameters of the system, and under some restrictions on parameters all solutions of initial boundary value problem for KS–GL equations tend to zero as with an exponential rate.

Keywords:

• structural stability
• continuous dependence
• Kuramoto-Sivashinsky–Ginzburg-Landau equations
• decay estimate

AMS Subject Classifications:

• 35B30; 35K55; 35Q35

Notes

The work of V. K. Kalantarov was supported in part by The Scientific and Research Council of Turkey, [grant number 112T934].