| Autor: |
Tobias Hacker, Guido Schneider, Hannes Uecker |
| Jazyk: |
angličtina |
| Rok vydání: |
2012 |
| Předmět: |
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| Zdroj: |
Electronic Journal of Differential Equations, Vol 2012, Iss 61,, Pp 1-51 (2012) |
| Druh dokumentu: |
article |
| ISSN: |
1072-6691 |
| Popis: |
The integral boundary layer system (IBL) with spatially periodic coefficients arises as a long wave approximation for the flow of a viscous incompressible fluid down a wavy inclined plane. The Nusselt-like stationary solution of the IBL is linearly at best marginally stable; i.e., it has essential spectrum at least up to the imaginary axis. Nevertheless, in this stable case we show that localized perturbations of the ground state decay in a self-similar way. The proof uses the renormalization group method in Bloch variables and the fact that in the stable case the Burgers equation is the amplitude equation for long waves of small amplitude in the IBL. It is the first time that such a proof is given for a quasilinear PDE with spatially periodic coefficients. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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