Buchot, Jean-Marie; Raymond, Jean-Pierre 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]. Cited in 11 Documents 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 Keywords:Crocco transformation; two dimensional Prandtl equations PDFBibTeX XMLCite \textit{J.-M. Buchot} and \textit{J.-P. Raymond}, ISNM, Int. Ser. Numer. Math. 139, 31--42 (2002; Zbl 1029.35029)