2004 | OriginalPaper | Buchkapitel
Quasilinear Boundary Layers: The Inner Layer ODE
verfasst von : Guy Métivier
Erschienen in: Small Viscosity and Boundary Layer Methods
Verlag: Birkhäuser Boston
Enthalten in: Professional Book Archive
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In this chapter we start the analysis of quasilinear equations. We study the ODE satisfied by stationary solutions that depend only on the normal variable. The admissible solutions w connect 0 at z = 0 to a bounded end state at z = +∞. The set C of those reachable end states is given by a central manifold theorem, which determines the boundary conditions associated to the limiting hyperbolic system. The local structure of C depends on transversality conditions or equivalently on stability conditions of the ODE.