## Bifurcation analysis of a coupled Kuramoto-Sivashinsky- and Ginzburg-Landau-type model.(English)Zbl 1397.35228

Summary: We study the bifurcation and stability of trivial stationary solution $$(0,0)$$ of coupled Kuramoto-Sivashinsky- and Ginzburg-Landau-type equations (KS-GL) on a bounded domain $$(0,L)$$ with Neumann’s boundary conditions. The asymptotic behavior of the trivial solution of the equations is considered. With the length $$L$$ of the domain regarded as bifurcation parameter, branches of nontrivial solutions are shown by using the perturbation method. Moreover, local behavior of these branches is studied, and the stability of the bifurcated solutions is analyzed as well.

### MSC:

 35Q35 PDEs in connection with fluid mechanics 35B32 Bifurcations in context of PDEs 35B35 Stability in context of PDEs 35Q56 Ginzburg-Landau equations
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