非自治非紧性多值随机动力系统的拉回吸引子的存在性，正则性和可测性

发布时间：2018-05-09 11:22

  本文选题：非紧性多值随机动力系统 + 拉回吸引子　； 参考：《兰州大学》2016年博士论文

【摘要】：在非紧性多值随机动力系统拉回吸引子的理论中,以非紧性测度为基础的渐近紧性方法,是用来证明拉回吸引子的存在性.首先,本文给出非自治非紧性多值随机动力系统拉回吸引子存在性的充分必要条件,给出拉回吸引子可测性的充分条件,并证明当随机系统包含周期或殆周期的确定性外力项时,拉回吸引子在一定的条件下也是周期或殆周期的.其次,在解不唯一的情形,研究定义在无界域上的具有非自治项和随机外力项的反应扩散方程,分别在空间L2(Rn),Lp(Rn)和H1(Rn)证明拉回吸引子存在,并且证明他们是相等的.通过验证映射ω→Φ(t,τ,ω,K(τ,ω))的某些性质,证明了拉回吸引子的可测性,其中K是闭可测的拉回吸收集.再次,以具有无穷时滞的半线性退化抛物方程为例,研究该方程生成的非自治非紧性多值随机动力系统,证明拉回吸引子的存在性和可测性.最后,以非自治振荡随机时滞波方程为例,方程中含有非线性记忆项和加性噪音,并假设非线性项是次临界增长的,考虑该方程生成的非自治非紧性多值随机动力系统,证明拉回吸引子的存在性和可测性.
[Abstract]:The asymptotic compactness method based on the measure of noncompactness is used to prove the existence of pull attractor in the theory of pull back attractor for multivalued stochastic dynamical systems with non-compactness. First of all, the sufficient and necessary conditions for the existence of pull back attractors for nonautonomous noncompact multivalued stochastic dynamical systems are given, and the sufficient conditions for the testability of pull back attractors are given. It is also proved that the pull back attractor is periodic or almost periodic under certain conditions when the stochastic system contains deterministic external force terms of periodic or almost periodic. Secondly, when the solution is not unique, the reaction-diffusion equations with nonautonomous term and random external force term defined on the unbounded domain are studied. In the space L _ 2N ~ (n) and H _ (1) R _ (n), the existence of pull back attractor is proved, and the existence of them is proved to be equal. By validating some properties of the mapping 蠅 _ n _ 桅 _ t, 蟿, 蠅 _ n _ K (蟿, 蠅 _ n), we prove the testability of the pull back attractor, where K is a closed measurable tractive absorption set. Thirdly, taking the semilinear degenerate parabolic equation with infinite delay as an example, the nonautonomous noncompact multivalued stochastic dynamical system generated by the equation is studied, and the existence and testability of the pull back attractor are proved. Finally, taking the nonautonomous oscillation stochastic delay wave equation as an example, the equation contains nonlinear memory term and additive noise, and assumes that the nonlinear term is subcritical growth. The nonautonomous noncompact multivalued stochastic dynamical system generated by the equation is considered. The existence and testability of pull back attractor are proved.
【学位授予单位】：兰州大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O175
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本文编号：1865828