Asymptotic behavior of stochastic fractional power dissipative equations on

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• 作者：Hong Lu^a ; ^{ljwenling@163.com" class="auth_mail" title="E-mail the corresponding author} ; Peter W. Bates^b ; ^{bates@math.msu.edu" class="auth_mail" title="E-mail the corresponding author} ; Jie Xin^c ; ^{fdxinjie@sina.com" class="auth_mail" title="E-mail the corresponding author} ; Mingji Zhang^d ; ^{mzhang@nmt.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：37L55 ; 35B40 ; 35B41
• 刊名：Nonlinear Analysis
• 出版年：2015
• 出版时间：November 2015
• 年：2015
• 卷：128
• 期：Complete
• 页码：176-198
• 全文大小：757 K

文摘

We study a reaction–fractional diffusion equation with additive noise on the entire space class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0362546X15002333&_mathId=si1.gif&_user=111111111&_pii=S0362546X15002333&_rdoc=1&_issn=0362546X&md5=abf5bb2717c5831de196ed875e8a521f" title="Click to view the MathML source">Rⁿclass="mathContainer hidden">class="mathCode">${\mathbb{R}}^n$ with particular interest in the asymptotic behavior of solutions. We first transform the equation into a random equation whose solutions generate a random dynamical system. A priori   estimates for solutions are derived when the nonlinearity satisfies certain growth conditions. Using estimates for far-field values of solutions and a cut-off technique, asymptotic compactness is proved. Thus, the existence of a random attractor in class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0362546X15002333&_mathId=si3.gif&_user=111111111&_pii=S0362546X15002333&_rdoc=1&_issn=0362546X&md5=871842f6ed6599c8008e95c6e081c61a" title="Click to view the MathML source">L²(Rⁿ)class="mathContainer hidden">class="mathCode">$L^2\left({\mathbb{R}}^n\right)$ is established.