一类随机波动方程的渐近行为
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摘要
本文主要讨论具有临界增长指数的强阻尼随机波动方程的渐近行为,通过使用加权范数,证明了对于任意的正强阻尼系数和耗散系数,该方程的解所确定的随机动力系统存在随机紧的吸引子。
This paper mainly studies the asymptotic behavior of strongly damped stochastic wave equations with critical growth exponent. By using weighted norm,for any positive strongly damped and diffusion coefficients,we prove that stochastic dynamical systems generated by the strongly damped stochastic wave equations with critical growth exponent exists a compact random attractor.
This paper mainly studies the asymptotic behavior of strongly damped stochastic wave equations with critical growth exponent. By using weighted norm,for any positive strongly damped and diffusion coefficients,we prove that stochastic dynamical systems generated by the strongly damped stochastic wave equations with critical growth exponent exists a compact random attractor.
引文
[1] ZHOU S F. Attractors for strongly damped wave equations with critical exponent[J]. Applied Mathematics Letters,2003,16:1307-1314.
[2] PATA V,ZELIK S. Smooth attractors for strongly damped wave equation[J]. Institute of Physics,2006,19:1495-1506.
[3]班爱玲,周盛凡.强阻尼的半线性波动方程全局吸引子的Hausdorff维数[J].上海师范大学学报(自然科学版),2008,37(3):234-237.
[4]尹福其,周盛凡,李红艳.具强阻尼的随机Sine-Gordon方程的随机吸引子存在性[J].上海大学学报(自然科学版),2006,12(3):260-265.
[5]郝红娟,周盛凡.具强阻尼的随机Sine-Gordon方程的随机吸引子存在性[J].上海师范大学学报(自然科学版),2010,39(2):121-129.
[6] FAN X M. Random attractor for a damped Sine-Gordon equation with white noise[J]. Pacific J Math,2004,216(1):63-76.
[7] CHUESHOV I,Monotone random systems theory and applications[M]. New York:Springer-Verlag,2002.
[8] BATES P W,LU K,WANG B. Random attractors for stochastic reaction diffusion equations on unbounded domains[J]. J Differential Equations,2009,246:845-869.
[9] DUAN J,LU K,SCHMALFUSS B. Invariant manifolds for stochastic partial differential equations[J]. Ann Probab,2003,31:2109-2135.
[10] TEMAM R. Infinite-dimensional dynamical systema in mechanics and physics[M]. New York:Springer-Verlag,1998.
[11] PAZY A. Semigroup of linear operators and applications to partial differential equations[M]. New York:Springer-Verlag,1983.
[12] SHEN Z,ZHOU S,SHEN W. One-dimensional random attractor and rotation number of the stochastic damped sine-Gordon equation[J]. J Differential Equations,2010,248:1432-1457.
[2] PATA V,ZELIK S. Smooth attractors for strongly damped wave equation[J]. Institute of Physics,2006,19:1495-1506.
[3]班爱玲,周盛凡.强阻尼的半线性波动方程全局吸引子的Hausdorff维数[J].上海师范大学学报(自然科学版),2008,37(3):234-237.
[4]尹福其,周盛凡,李红艳.具强阻尼的随机Sine-Gordon方程的随机吸引子存在性[J].上海大学学报(自然科学版),2006,12(3):260-265.
[5]郝红娟,周盛凡.具强阻尼的随机Sine-Gordon方程的随机吸引子存在性[J].上海师范大学学报(自然科学版),2010,39(2):121-129.
[6] FAN X M. Random attractor for a damped Sine-Gordon equation with white noise[J]. Pacific J Math,2004,216(1):63-76.
[7] CHUESHOV I,Monotone random systems theory and applications[M]. New York:Springer-Verlag,2002.
[8] BATES P W,LU K,WANG B. Random attractors for stochastic reaction diffusion equations on unbounded domains[J]. J Differential Equations,2009,246:845-869.
[9] DUAN J,LU K,SCHMALFUSS B. Invariant manifolds for stochastic partial differential equations[J]. Ann Probab,2003,31:2109-2135.
[10] TEMAM R. Infinite-dimensional dynamical systema in mechanics and physics[M]. New York:Springer-Verlag,1998.
[11] PAZY A. Semigroup of linear operators and applications to partial differential equations[M]. New York:Springer-Verlag,1983.
[12] SHEN Z,ZHOU S,SHEN W. One-dimensional random attractor and rotation number of the stochastic damped sine-Gordon equation[J]. J Differential Equations,2010,248:1432-1457.