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A linearized model for boundary layer equations. (English) Zbl 1029.35029

Hoffmann, K.-H. (ed.) et al., Optimal control of complex structures. Proceedings of the international conference, Oberwolfach, Germany, June 4-10, 2000. Basel: Birkhäuser. ISNM, Int. Ser. Numer. Math. 139, 31-42 (2002).
Summary: By using the so-called Crocco transformation, the two dimensional Prandtl equations, which are stated in an unbounded domain, are transformed into a nonlinear degenerate parabolic equation (the Crocco equation) stated in a domain \(\Omega\times (0,T)=] 0,L[\times] 0,1[\times(0,T)\). In this paper, we study a degenerate parabolic equation in \(\Omega\times(0,T)\) coming from the linearization of the Crocco equation. This is a crucial step to next construct feedback control laws to settle stabilization problems.
For the entire collection see [Zbl 0997.00022].

MSC:

35B35 Stability in context of PDEs
35K65 Degenerate parabolic equations
35K55 Nonlinear parabolic equations
76D10 Boundary-layer theory, separation and reattachment, higher-order effects
76D55 Flow control and optimization for incompressible viscous fluids
93C20 Control/observation systems governed by partial differential equations
35A22 Transform methods (e.g., integral transforms) applied to PDEs
93D15 Stabilization of systems by feedback
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