An extension of the classical parabolized stability equations to flows strongly dependent on the two cross-stream spatial directions and weakly dependent on the streamwise one is applied to model the large-scale structures ...

This work presents feedback designs of exponentially stabilizing boundary controllers for a one-dimensional system coupling elliptic and parabolic equations. The control acts on one Dirichlet boundary condition of the ...

We study the convergence of the statistical solutions of the parabolic equation. Under some mixing condition (in the sense of Rosenblatt) for initial measure and natural assumptions on the coefficients of the equation we ...