本文選題：非緊性多值隨機(jī)動(dòng)力系統(tǒng) + 拉回吸引子�。� 參考：《蘭州大學(xué)》2016年博士論文

【摘要】：在非緊性多值隨機(jī)動(dòng)力系統(tǒng)拉回吸引子的理論中,以非緊性測(cè)度為基礎(chǔ)的漸近緊性方法,是用來證明拉回吸引子的存在性.首先,本文給出非自治非緊性多值隨機(jī)動(dòng)力系統(tǒng)拉回吸引子存在性的充分必要條件,給出拉回吸引子可測(cè)性的充分條件,并證明當(dāng)隨機(jī)系統(tǒng)包含周期或殆周期的確定性外力項(xiàng)時(shí),拉回吸引子在一定的條件下也是周期或殆周期的.其次,在解不唯一的情形,研究定義在無界域上的具有非自治項(xiàng)和隨機(jī)外力項(xiàng)的反應(yīng)擴(kuò)散方程,分別在空間L2(Rn),Lp(Rn)和H1(Rn)證明拉回吸引子存在,并且證明他們是相等的.通過驗(yàn)證映射ω→Φ(t,τ,ω,K(τ,ω))的某些性質(zhì),證明了拉回吸引子的可測(cè)性,其中K是閉可測(cè)的拉回吸收集.再次,以具有無窮時(shí)滯的半線性退化拋物方程為例,研究該方程生成的非自治非緊性多值隨機(jī)動(dòng)力系統(tǒng),證明拉回吸引子的存在性和可測(cè)性.最后,以非自治振蕩隨機(jī)時(shí)滯波方程為例,方程中含有非線性記憶項(xiàng)和加性噪音,并假設(shè)非線性項(xiàng)是次臨界增長(zhǎng)的,考慮該方程生成的非自治非緊性多值隨機(jī)動(dòng)力系統(tǒng),證明拉回吸引子的存在性和可測(cè)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.
【學(xué)位授予單位】：蘭州大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：O175
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本文編號(hào)：1865828