scholarly journals Random attractors for non-autonomous stochastic wave equations with multiplicative noise

2014 ◽  
Vol 34 (1) ◽  
pp. 269-300 ◽  
Author(s):  
Bixiang Wang ◽  
Keyword(s):  
Wave Equations ◽  
Multiplicative Noise ◽  
Stochastic Wave Equations ◽  
Random Attractors

RANDOM ATTRACTORS FOR DAMPED STOCHASTIC WAVE EQUATIONS WITH MULTIPLICATIVE NOISE

2008 ◽  
Vol 19 (04) ◽  
pp. 421-437 ◽  
Author(s):  
XIAOMING FAN
Keyword(s):  
Fractal Dimension ◽  
Dynamical Systems ◽  
Wave Equations ◽  
Multiplicative Noise ◽  
Random Dynamical Systems ◽  
Stochastic Wave Equations ◽  
Random Attractors

In this paper, we investigate the existence of compact random attractors and their fractal dimension for the random dynamical systems determined by damped stochastic wave equations of Sine–Gordon type with linear multiplicative noise.

scholarly journals Full Discretization of Semilinear Stochastic Wave Equations Driven by Multiplicative Noise

2016 ◽  
Vol 54 (2) ◽  
pp. 1093-1119 ◽  
Author(s):  
Rikard Anton ◽  
David Cohen ◽  
Stig Larsson ◽  
Xiaojie Wang
Keyword(s):  
Wave Equations ◽  
Multiplicative Noise ◽  
Full Discretization ◽  
Stochastic Wave Equations

scholarly journals Weak Convergence Rates for Spatial Spectral Galerkin Approximations of Semilinear Stochastic Wave Equations with Multiplicative Noise

2021 ◽  
Author(s):  
Ladislas Jacobe de Naurois ◽  
Arnulf Jentzen ◽  
Timo Welti
Keyword(s):  
Wave Equation ◽  
Weak Convergence ◽  
Wave Equations ◽  
Multiplicative Noise ◽  
Convergence Rates ◽  
Rates Of Convergence ◽  
Kolmogorov Equation ◽  
Continuous Version ◽  
Stochastic Wave Equations ◽  
Galerkin Approximations

AbstractStochastic wave equations appear in several models for evolutionary processes subject to random forces, such as the motion of a strand of DNA in a liquid or heat flow around a ring. Semilinear stochastic wave equations can typically not be solved explicitly, but the literature contains a number of results which show that numerical approximation processes converge with suitable rates of convergence to solutions of such equations. In the case of approximation results for strong convergence rates, semilinear stochastic wave equations with both additive or multiplicative noise have been considered in the literature. In contrast, the existing approximation results for weak convergence rates assume that the diffusion coefficient of the considered semilinear stochastic wave equation is constant, that is, it is assumed that the considered wave equation is driven by additive noise, and no approximation results for multiplicative noise are known. The purpose of this work is to close this gap and to establish essentially sharp weak convergence rates for spatial spectral Galerkin approximations of semilinear stochastic wave equations with multiplicative noise. In particular, our weak convergence result establishes as a special case essentially sharp weak convergence rates for the continuous version of the hyperbolic Anderson model. Our method of proof makes use of the Kolmogorov equation and the Hölder-inequality for Schatten norms.

scholarly journals Random attractors for Stochastic strongly damped non-autonomous wave equations with memory and multiplicative noise

2019 ◽  
Vol 3 (2) ◽  
pp. 50-70
Author(s):  
Abdelmajid Ali Dafallah ◽  
◽  
Qiaozhen MA ◽  
Ahmed Eshag Mohamed ◽  
◽  
...  
Keyword(s):  
Wave Equations ◽  
Multiplicative Noise ◽  
Random Attractors ◽  
With Memory ◽  
Strongly Damped
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