Zobrazeno 1 - 10
of 83
pro vyhledávání: '"Kostianko, Anna"'
Autor:
Kostianko, Anna, Zelik, Sergey
We develop the attractors theory for the semigroups with multidimensional time belonging to some closed cone in an Euclidean space and apply the obtained general results to partial differential equations (PDEs) in unbounded domains. The main attentio
Externí odkaz:
http://arxiv.org/abs/2208.01727
Reaction-diffusion systems with mass dissipation are known to possess blow-up solutions in high dimensions when the nonlinearities have super quadratic growth rates. In dimension one, it has been shown recently that one can have global existence of b
Externí odkaz:
http://arxiv.org/abs/2205.02498
We study the Kolmogorov's entropy of uniform attractors for non-autonomous dissipative PDEs. The main attention is payed to the case where the external forces are not translation-compact. We present a new general scheme which allows us to give the up
Externí odkaz:
http://arxiv.org/abs/2202.05590
We discuss the estimates for the $L^p$-norms of systems of functions that are orthonormal in $L^2$ and $H^1$, respectively, and their essential role in deriving good or even optimal bounds for the dimension of global attractors for the classical Navi
Externí odkaz:
http://arxiv.org/abs/2202.01531
We study the global attractors for the damped 3D Euler--Bardina equations with the regularization parameter $\alpha>0$ and Ekman damping coefficient $\gamma>0$ endowed with periodic boundary conditions as well as their damped Euler limit $\alpha\to0$
Externí odkaz:
http://arxiv.org/abs/2112.13691
We study the properties of linear and non-linear determining functionals for dissipative dynamical systems generated by PDEs. The main attention is payed to the lower bounds for the number of such functionals. In contradiction to the common paradigm,
Externí odkaz:
http://arxiv.org/abs/2111.04125
We prove existence of the global attractor of the damped and driven Euler--Bardina equations on the 2D sphere and on arbitrary domains on the sphere and give explicit estimates of its fractal dimension in terms of the physical parameters.
Externí odkaz:
http://arxiv.org/abs/2107.10779
We prove the existence of an Inertial Manifold for 3D complex Ginzburg-Landau equation with periodic boundary conditions as well as for more general cross-diffusion system assuming that the dispersive exponent is not vanishing. The result is obtained
Externí odkaz:
http://arxiv.org/abs/2106.10538
The dependence of the fractal dimension of global attractors for the damped 3D Euler--Bardina equations on the regularization parameter $\alpha>0$ and Ekman damping coefficient $\gamma>0$ is studied. We present explicit upper bounds for this dimensio
Externí odkaz:
http://arxiv.org/abs/2106.09077
Autor:
Kostianko, Anna, Zelik, Sergey
The paper is devoted to a comprehensive study of smoothness of inertial manifolds for abstract semilinear parabolic problems. It is well known that in general we cannot expect more than $C^{1,\varepsilon}$-regularity for such manifolds (for some posi
Externí odkaz:
http://arxiv.org/abs/2102.03473