Random Attractors Of The Stochastic Generalized Kuramoto-Sivashinsky Equation With Interferences

The problems of the existence of random attractors for the stochastic gener-alized kuramoto-sivashinsky equation with multiplicative noise and with additive noise in L2space, the problem of the existence of random attractor for the stochas-tic generalized k-s equation with additive noise on unbounded domains Rn. The paper contains four parts as following:In charter one, the background on the of RDS and global attractor, main con-tents that we will discuss and significance are introduced.In charter two, to the K-S equation a multiplicative noise is introduced,based on periodic and with initial conditions in L2space. To prove the existence theorems of random attractor for the stochastic dynamical system generated by the solution of the generalized K-S equation. These results extend the existence theorems of random attractors of some generalized differential equations with multiplicative noise on the uniqueness of the solution generated by the stochastic dynamic system in L2space.In charter three, to the K-S equation an additive noise is introduced,based on periodic and with initial conditions in L2space. To prove the existence theorems of random attractor for the stochastic dynamical system generated by the solution of the generalized K-S equation. These results extend the existence theorems of random attractors of some generalized differential equations with additive noise on the uniqueness of the solution generated by the stochastic dynamic system in L2space. In charter four, to the K-S equation an additive noise is introduced on unbound-ed domains Rn with some constrains on some items and coefficient. To prove the existence theorems of random attractor for the stochastic dynamical system gen-erated by the solution of the generalized K-S equation. These results extend the existence theorems of random attractors of some generalized differential equations with additive noise on the uniqueness of the solution generated by the stochastic dynamic system on unbounded domains Rn.