Uniform trajectory attractor for non-autonomous reaction–diffusion equations with Carathéodory’s nonlinearity

Gorban, Nataliia V.; Kapustyan, O. V.; Kasyanov, Pavlo O.

doi:10.1016/j.na.2013.12.004

Cited by 31 publications

(15 citation statements)

References 14 publications

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“…There has been many literature on the trajectory attractors [3,7,[14][15][16][17]19]. First, Chepyzhow et al [4,5] study the following 3D Navier-Stokes-α model, 5) and showed that the trajectory attractor of the Navier-Stokes-α model converges to the trajectory attractor of the 3D Navier-Stokes system as α → 0 + .…”

Section: Introductionmentioning

confidence: 99%

Upper Semicontinuity of Trajectory Attractors for 3D Incompressible Navier–Stokes Equation

Qin

Wang

2019

Appl Math Optim

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Section: Introductionmentioning

confidence: 99%

Upper Semicontinuity of Trajectory Attractors for 3D Incompressible Navier–Stokes Equation

Qin

Wang

2019

Appl Math Optim

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“…Note that for each γ > 1, every translation bounded in L loc γ (R + ) function is t.u.i. in L loc 1 (R + ); Gorban et al [13].…”

Section: Main Constructions and Resultsmentioning

confidence: 99%

Uniform Global Attractors for Non-autonomous Dissipative Dynamical Systems

Zgurovsky

Gluzman

Gorban³

et al. 2017

Qualitative and Quantitative Analysis of Nonlinear Systems

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In this paper we consider sufficient conditions for the existence of uniform compact global attractor for non-autonomous dynamical systems in special classes of infinite-dimensional phase spaces. The obtained generalizations allow us to avoid the restrictive compactness assumptions on the space of shifts of non-autonomous terms in particular evolution problems. The results are applied to several evolution inclusions. D R A F T

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“…This is a weakly compact set in L loc 1 (R + ); Gorban et al [6]. Let us consider the family of problems…”

Section: Proof Of Theorem 131mentioning

confidence: 99%

Uniform Trajectory Attractors for Nonautonomous Dissipative Dynamical Systems

Zgurovsky

Kasyanov

2015

Studies in Systems, Decision and Control

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For all global weak solutions of the general classes of nonautonomous evolution equations and inclusions that satisfy standard sign and polynomial growth conditions, the multivalued dynamics as time t → +∞ is studied. The existence of a compact uniform trajectory attractor is justified. The obtained results allow to investigate long-time behavior of distributions of state functions for various mathematical models in geophysics, mechanics, biology, medicine etc.

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Uniform trajectory attractor for non-autonomous reaction–diffusion equations with Carathéodory’s nonlinearity

Cited by 31 publications

References 14 publications

Upper Semicontinuity of Trajectory Attractors for 3D Incompressible Navier–Stokes Equation

Upper Semicontinuity of Trajectory Attractors for 3D Incompressible Navier–Stokes Equation

Uniform Global Attractors for Non-autonomous Dissipative Dynamical Systems

Uniform Trajectory Attractors for Nonautonomous Dissipative Dynamical Systems

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