17 citations · 39 across the 18 of their papers we have counts for
5 papers · 1 filter
Inertial manifolds via spatial averaging revisited
Anna Kostianko, Xinhua Li, Chunyou Sun +1
The paper gives a comprehensive study of inertial manifolds for semilinear parabolic equations and their smoothness using the spatial averaging method suggested by G. Sell and J. M…
Reaction-diffusion systems with supercritical nonlinearities revisited
Anna Kostianko, Chunyou Sun, Sergey Zelik
We give a comprehensive study of the analytic properties and long-time behavior of solutions of a reaction-diffusion system in a bounded domain in the case where the nonlinearity s…
Validity of the hyperbolic Whitham modulation equations in Sobolev spaces
Thomas J. Bridges, Anna Kostianko, Sergey Zelik
It is proved that modulation in time and space of periodic wave trains, of the defocussing nonlinear Schrödinger equation, can be approximated by solutions of the Whitham modulatio…
A proof of validity for multiphase Whitham modulation theory
Tom Bridges, Anna Kostianko, Guido Schneider
It is proved that approximations which are obtained as solutions of the multiphase Whitham modulation equations stay close to solutions of the original equation on a natural time s…
Bi-Lipschitz Mane projectors and finite-dimensional reduction for complex Ginzburg-Landau equation
Anna Kostianko
We present a new method of establishing the finite-dimensionality of limit dynamics (in terms of bi-Lipschitz Mane projectors) for semilinear parabolic systems with cross diffusion…