Upper Semicontinuity Of Pullback Attractors For Non-Autonomous Lattice Systems Under Singular Perturbations

In this thesis,we mainly consider the upper semicontinuity of the global pullback attractors for the second order nonautonomous lattice systems with singular perturbations about the coefficient of the second order term.In the first chapter,we first introduce the background of the research,then we introduce the main work of this thesis,and the preparatory knowledge is given at last.In the second chapter,we prove that the second order nonautonomous lattice sys-tems with singular perturbations and the corresponding first order nonautonomous lattice systems have pullback attractors under certain conditions,respectively.In the third chapter,we consider the upper semicontinuity of global pullback at-tractors with respect to the coefficient of second order derivative term under Hausdorff semidistance.(ⅰ)We study the relationship between the global pullback attractors for second order nonautonomous lattice system and the global pullback attractor for the corresponding first order nonautonomous lattice system when the coefficient of second derivation term tends to zero.We construct a family of compact sets in the phase space of the second order nonautonomous lattice systems such that each sections of the pull-back attractor of the first order nonautonomous lattice system is naturally embedded into these sets as the first components,and prove that each sections of the global pullback attractors for second order nonautonomous lattice system can enter any neighborhood of these compact sets when the coefficient of second derivation term is small enough;(ⅱ)we prove that the upper semicontinuity of the pullback attractors of second order nonautonomous lattice systems at positive coefficient of second derivative term.In the fourth chapter,we consider the existence,exponentially stability and upper semicontinuity of the singleton pullback attractor for the second order and first order nonautonomous lattice systems under certain conditions,respectively.