非自治随机Sine-Gordon方程组的拉回动力行为
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摘要
主要研究了带加法扰动的非自治随机Sine-Gordon方程组的拉回动力行为,通过对解的一致估计证明了方程组产生的随机动力系统在空间(H_0~1(O)×L~2(O))~2上存在唯一的拉回吸引子.
We are interested in the pullback dynamics for non-autonomous stochastic Sine-Gordon equations with an additive noise.By the use of the uniform estimates of solutions,we prove the existence of a unique pullback attractor for the random dynamical system generated by non-autonomous stochastic Sine-Gordon equations defined in(H_0~1(O)×L~2(O))~2.
We are interested in the pullback dynamics for non-autonomous stochastic Sine-Gordon equations with an additive noise.By the use of the uniform estimates of solutions,we prove the existence of a unique pullback attractor for the random dynamical system generated by non-autonomous stochastic Sine-Gordon equations defined in(H_0~1(O)×L~2(O))~2.
引文
[1]赵月利,李扬荣,贺军可.带加法扰动的随机Sine-Gordon方程组的随机吸引子[J].西南师范大学学报(自然科学版),2012,37(6):32-36.
[2]FAN X M.Random Attractors for a Damped Sine-Gordon Equations with White Noise[J].Pacific J Math.2004,216(1):63-76.
[3]尹福其,刘林芳,肖翠辉.无界区域非自治随机Sine-Gordon方程的D-周期吸引子[J].数学学报,2014,57(6):1127-1140.
[4]WANG B X.Sufficient and Necessary Criteria for Existence of Pullback Attractors for Non-Compact Random Dynamical Systems[J].Journal of Differential Equations,2012,253(5):1544-1583.
[5]LI Y R,GUO B L.Random Attractors for Quasi-Continuous Random Dynamical Systems and Applications to Stochastic Reaction-Diffusion Equations[J].Journal of Differential Equations,2008,245(7):1775-1800.
[6]CUI H Y,LANGA J A,LI Y R,Regularity and Structure of Pullback Attractors for Reaction Diffusion Type Systems without Uniqueness[J].Nonlinear Analysis,2016,140:208-235.
[7]赵文强.带加法白噪音的随机Boussinesq方程组的解的渐近行为[J].数学学报,2013,56(1):1-14.
[8]PAZY A.Semigroups of Linear Operators and Applications to Partial Differential Equations[M].Berlin:Springer-Verlag,1983.
[2]FAN X M.Random Attractors for a Damped Sine-Gordon Equations with White Noise[J].Pacific J Math.2004,216(1):63-76.
[3]尹福其,刘林芳,肖翠辉.无界区域非自治随机Sine-Gordon方程的D-周期吸引子[J].数学学报,2014,57(6):1127-1140.
[4]WANG B X.Sufficient and Necessary Criteria for Existence of Pullback Attractors for Non-Compact Random Dynamical Systems[J].Journal of Differential Equations,2012,253(5):1544-1583.
[5]LI Y R,GUO B L.Random Attractors for Quasi-Continuous Random Dynamical Systems and Applications to Stochastic Reaction-Diffusion Equations[J].Journal of Differential Equations,2008,245(7):1775-1800.
[6]CUI H Y,LANGA J A,LI Y R,Regularity and Structure of Pullback Attractors for Reaction Diffusion Type Systems without Uniqueness[J].Nonlinear Analysis,2016,140:208-235.
[7]赵文强.带加法白噪音的随机Boussinesq方程组的解的渐近行为[J].数学学报,2013,56(1):1-14.
[8]PAZY A.Semigroups of Linear Operators and Applications to Partial Differential Equations[M].Berlin:Springer-Verlag,1983.