Abstract:

Two algorithms are presented that allow one to find initial data for asymptotically stable solutions to Cauchy problems for ODE systems that are increasing over the initial time interval. One algorithm uses eigenvectors, while the other is based on the matrix spectrum dichotomy method. Using these algorithms, locally increasing solutions were constructed for the flutter models and the Navier-Stokes system linearized in the neighborhood of plane-parallel Poiseuille flow. A two-sided estimate for the maximum norm of these solutions was obtained.