Random Attractor For Delayed Random Wave Equations And Its Hausdorff Dimension

In this paper,we mainly study the retarded random waved equation and with the following initial conditions Where B(ut,θ(t)ω) is the source intensity which may depend on the history of the solution. u, is defined for σ∈[-r,0], asut=ut(σ)=u(t+σ).Where r>0describes retarded time. θt in the equation is a group of measure-preserving and ergodic transformations,where{θt,t∈R}:θ,w(·)=w(·+t)-w(t). w(t) in the equation is a random term,and it describes a additive noise.Retarded random waved equation mainly reflects in this fields,such as acoustics electromagnetism and fluid mechanics.This paper mainly consists of the following four chapters discussing the behavior of solution of the retarded random waved equation:In the first chapter,mainly introduces retarded random dynamical systems and the study background and situation of retarded random waved equation,In the second chapter,mainly introduces some basic concepts and commonly used inequalities,In the third chapter,mainly discusses the existence and uniqueness of solutions of the retarded random waved equation,and proves the existence of retarded random attractor for the retarded random waved equation,In the fourth chapter,mainly discusses the retarded Hausdorff dimension of retarded random attractor for the retarded random waved equation.