Existence And Fractal Dimension Estimation Of Exponential Attractors For Impulsive Dynamical Systems

The theory of pulsed dynamical system is the key to simulate the real problem and plays an important role in the mathematical model.In this paper,the global attractor and exponential attractor were defined on the basis of the Impulsive dynamical system,and constructed the exponential attractor as well as proved its existence theorems.The second chapter introduces the concepts of global attractor and exponential attractor and their related properties,and then introduces the properties of semigroups generated by impulse dynamical system and the concept of noncompactness measure and its related properties.In the third chapter,based on that we have obtained exponential attractors with finite fractal dimension of continuous dynamical system applying the method of continuous mapping make discrete iteration,we discuss the existence of exponential attractors for dissipative evolution equations of first order when the nonlinear term R is C¹and there exist constants C>0 and for any constant p>1 only depend on X,satisfying|DR(u)|?C(|u|^p-1+1)for any u?X.In the fourth chapter,the concepts of exponential attractor in the pulsed dynamical system is defined firstly,then the conditions that the pulsed semigroup satisfies the squeezing property of general semigroup are analyzed and the construction of exponential attractor in the pulsed dynamical system is studied,and its fractal dimension and exponential convergence rate are estimated.On basis of the fourth chapter,the fifth chapter discusses the squeezing property and the existence of exponential attractors for dissipative evolution equations of first order with impulsive function.The sixth chapter,firstly,gives the global exponential k-dissipative semigroup in impulsive dynamical system,and then proves the existence global attractor under the condition of global exponentially k-dissipative in impulsive dynamical system,and constructs the exponential attractor and estimates the convergence rate of the attractor,fractal dimension,pre-compactness.