随机Zakharov格点方程的后向紧随机吸引子

Backward Compact Random Attractors for Stochastic Zakharov Lattice Equation

在对外力后向缓增的假设条件下,通过对解的估计,首先证明了具有乘法噪音的随机Zakharov格点方程在空间E=l^(2)×l^(2)×l^(2)上存在后向紧一致吸收集,再证明了由该方程生成的随机动力系统在吸收集上是后向渐进紧的.最后利用后向紧吸引子的存在性定理,证明了该随机Zakharov格点方程在空间E=l^(2)×l^(2)×l^(2)上存在后向紧随机吸引子.

When the external force is backward tempered,by estimating the solution,it is first proved that the random Zakharov lattice equation with multiplicative noise has backward compact uniformly absorbing set on the space E=l^(2)×l^(2)×l^(2),then it is proved that the random dynamical system generated by this equation is backward asymptotically compact on the absorbing set.Finally,by the Existence theorem of backward compact attractors,it is proved that there exists a backward compact random attractor for the stochastic Zakharov lattice equation in the space E=l^(2)×l^(2)×l^(2).