Finite fractal dimension of random attractor for stochastic non-autonomous strongly damped wave equation

Abstract In this paper, we first prove the existence of a random attractor for stochastic non-autonomous strongly damped wave equations with additive white noise. Then we apply a criteria to obtain an upper bound of fractal dimension of the random attractor of considered system.

[1]  B. Guo,et al.  Long Time Behavior of Strongly Damped Nonlinear Wave Equations , 1998 .

[2]  Gang Wang,et al.  Fractal Dimension of a Random Invariant Set and Applications , 2013, J. Appl. Math..

[3]  Bixiang Wang,et al.  Sufficient and Necessary Criteria for Existence of Pullback Attractors for Non-compact Random Dynamical Systems , 2012, 1202.2390.

[4]  Shengfan Zhou,et al.  Random attractor for stochastic non-autonomous damped wave equation with critical exponent , 2016 .

[5]  Bixiang Wang Random attractors for non-autonomous stochasticwave equations with multiplicative noise , 2013 .

[6]  Shengfan Zhou,et al.  Fractal dimension of random attractor for stochastic non-autonomous damped wave equation with linear multiplicative white noise , 2015 .

[7]  R. Temam Infinite Dimensional Dynamical Systems in Mechanics and Physics Springer Verlag , 1993 .

[8]  Shengfan Zhou,et al.  Fractal dimension of random attractors for stochastic non-autonomous reaction-diffusion equations , 2016, Appl. Math. Comput..

[9]  P. Massatt Limiting behavior for strongly damped nonlinear wave equations , 1983 .

[10]  Xiaoming Fan RANDOM ATTRACTORS FOR DAMPED STOCHASTIC WAVE EQUATIONS WITH MULTIPLICATIVE NOISE , 2008 .

[11]  Shengfan Zhou,et al.  Attractors for strongly damped wave equations with critical exponent , 2003, Appl. Math. Lett..

[12]  Ke Li,et al.  Exponential attractors for the strongly damped wave equation , 2013, Appl. Math. Comput..

[13]  Shengfan Zhou,et al.  On non-autonomous strongly damped wave equations with a uniform attractor and some averaging☆ , 2008 .

[14]  Peter E. Kloeden,et al.  Asymptotic behavior of solutions for random wave equations with nonlinear damping and white noise , 2011 .

[15]  Shengfan Zhou,et al.  Random attractor of the stochastic strongly damped wave equation , 2012 .

[16]  L. Arnold Random Dynamical Systems , 2003 .

[17]  Jean-Michel Ghidaglia,et al.  Longtime behaviour of strongly damped wave equations, global attractors and their dimension , 1991 .

[18]  Yangrong Li,et al.  Backwards compact attractors and periodic attractors for non-autonomous damped wave equations on an unbounded domain , 2017, Comput. Math. Appl..

[19]  Shengfan Zhou,et al.  Random Attractor for Non-autonomous Stochastic Strongly Damped Wave Equation on Unbounded Domains , 2015 .

[20]  Ban Ai-lin Global Attractor for Strongly Damped Nonlinear Wave Equation , 2014 .

[21]  Chunyou Sun,et al.  Dynamics of strongly damped wave equations in locally uniform spaces: Attractors and asymptotic regularity , 2008 .

[22]  Shengfan Zhou,et al.  Fractal dimension of random invariant sets for nonautonomous random dynamical systems and random attractor for stochastic damped wave equation , 2016 .

[23]  Sergey Zelik,et al.  Finite-dimensional attractors for the quasi-linear strongly-damped wave equation , 2008, 0807.5078.

[24]  R. Jones,et al.  Asymptotic behavior of a class of stochastic nonlinear wave equations with dispersive and dissipative terms , 2013 .

[25]  Xiaoming Fan,et al.  Kernel sections for non-autonomous strongly damped wave equations , 2002 .

[26]  Shengfan Zhou Dimension of the global attractor for strongly damped nonlinear wave equation , 1999 .

[27]  James C. Robinson,et al.  Fractal dimension of a random invariant set , 2006 .