Abstract
In this paper, an upper bound of fractal dimension of the compact kernel sections for the dissipative non-autonomous Klein-Gordon-Schrödinger lattice system is obtained, by applying a criterion for estimating fractal dimension of a family of compact subsets of a separable Hilbert space.
Highlights
Compact Kernel Sections, Dissipative, Fractal Dimension, Non-Autonomous, Klein-Gordon-Schrödinger Lattice System
In view of this point, this paper is to estimate the fractal dimension of the compact kernel sections for the dissipative non-autonomous KGS lattice system (1.1)
In the sequel of this paper, we will present a criterion for estimating the fractal dimension of a family of compact subsets of a separable Hilbert space and apply this criterion to obtain an upper bound of the fractal dimension of the compact kernel sections associated with the dissipative non-autonomous KGS lattice system (1.1)
Summary
Compact Kernel Sections, Dissipative, Fractal Dimension, Non-Autonomous, Klein-Gordon-Schrödinger Lattice System The existence of uniform exponential attractors for the dissipative non-autonomous KGS lattice system (1.1) with quasi-periodic symbols is studied in weighted spaces of infinite sequences by Abdallah in [27], simultaneously, some main results that the solution semigroup associated with such a system is Lipschitz continuous, α-contraction and satisfies the squeezing property, are obtained under some premise.
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