Quasilinear Boundary Layers: The Inner Layer ODE
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.
KeywordsFixed Point Theorem Implicit Function Theorem Burger Equation Bounded Solution Transversality Condition
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