带Neumann边界条件的3维随机 Ginzburg-Landau方程的渐近行为

Asymptotic Behavior for the 3-Dimensional Stochastic Ginzburg-Landau Equation with Neumann Boundary Conditions

摘要: Ginzburg-Landau方程应用于一些物理领域, 如流体力学,波传播等. 同时, 作为一类抛物方程模型它在数学领域也受到关注. 文章旨在研究3维空间中带非齐次Neumann边界条件的随机广义Ginzburg-Landau方程的渐近行为, 通过证明方程产生的随机动力系统在空间H和空间V中存在吸收集, 证明了该系统在空间H中随机吸引子的存在性

Abstract: Ginzburg-Landau equation can find application in some domains of physics like fluid mechanics and wave propagation; and it attracts attention in the field of mathematics as a model of parabolic equation. The asymptotic behavior for the stochastic generalized Ginzburg-Landau equation with inhomogeneous Neumann boundary conditions is examined in the 3-dimensional space. It is proved that the stochastic dynamical system possesses a random attracting set in spaceH and V and the said system exists the random attractors in spaceH