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Stable invariant manifolds with application to control problems

  • * Corresponding author: Alexey Gorshkov

    * Corresponding author: Alexey Gorshkov

This article was recruited by Andrii Mironchenko

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  • In this article we develop the theory of stable invariant manifolds for evolution equations with application to control problem. We will construct invariant subspaces for linear equations which can be extended to the non-linear equations in the neighbourhood of the equilibrium with help of perturbation theory. Here will be considered both cases of the discrete and continuous spectrum of the generator associated with resolving semi-group. The example of global invariant manifold will be presented for Burgers equation.

    Mathematics Subject Classification: Primary: 37D10; Secondary: 93D15.


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