The Long Time Behavior Of Stochastic P-laplacian Equations

There are two topics studied in this paper.Firstly,the existence and unique-ness of the weak mean random attractors in L2 for mean random dynamical systems derived from the non-autonomous stochastic p-Laplacian equations with nonlinear noise and the random pull-back attractors in L2 for the cocycles derived from the non-autonomous stochastic p-Laplacian equations with linear multiplicative noise are studied respectively.Secondly,we also investigate the existence and uniqueness of the random pull-back attractors in Lp for random dynamical systems generated by the autonomous equations with linear multiplicative noise and the existence of the exponential attractors in L2 for the semigroups derived from the autonomous equations(when p=2)with linear multiplicative noise.The first chapter mainly introduces the research background and current situ-ation of RDSs and briefly summarizes the main work of this paper.In chapter two,the mathematical framework of stochastic p-Laplace equations is described and its well-posedness is proved.Chapter three is devoted to the existence and uniqueness of the weak mean random attractors in L2 for mean random dynamical system derived from stochas-tic p-Laplacian equations with the nonlinear diffusion coefficient.In chapter four,we establish the existence and uniqueness of the random pull-back attractors in L2 for the cocycles generated by stochastic p-Laplacian equations with linear multiplicative noise.There are two subsections in chapter five.the existence and uniqueness of the random pull-back attractors in Lp for the RDSs generated by the autonomous form of stochastic p-Laplacian equations with linear multiplicative noise is proved in sec-tion 5.1.And the exponential attractors in L2 for the semigroups derived from the autonomous equations(when p=2)with linear multiplicative noise is constructed in section 5.2.