14 citations · 59 across the 15 of their papers we have counts for
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Inertial manifolds and foliations for asymptotically compact cocycles in Banach spaces
Mikhail Anikushin
We study asymptotically compact nonautonomous dynamical systems given by abstract cocycles in Banach spaces. Our main assumptions are given by a squeezing property in a quadratic c…
Frequency theorem for parabolic equations and its relation to inertial manifolds theory
Mikhail Anikushin
We obtain a version of the Frequency Theorem (a theorem on solvability of certain operator inequalities), which allows to construct quadratic Lyapunov functionals for semilinear pa…
Nonlinear semigroups for delay equations in Hilbert spaces, inertial manifolds and dimension estimates
Mikhail Anikushin
We study the well-posedness of nonautonomous nonlinear delay equations in as evolutionary equations in a proper Hilbert space. We present a construction of solving…
Frequency theorem and inertial manifolds for neutral delay equations
Mikhail Anikushin
We study the quadratic regulator problem for linear control systems in Hilbert spaces, where the cost functional is in some sense unbounded. Our motivation comes from delay equatio…
The Poincaré-Bendixson theory for certain compact semi-flows in Banach spaces
Mikhail Anikushin
We study semiflows satisfying a certain squeezing condition with respect to a quadratic functional in some Banach space. Under certain compactness assumptions from our previous res…