Asymptotic Behavior of Stochastic Wave Equations with Critical Exponents on R³

2008/10/11 by Bixiang Wang, Wang, Bixiang · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Stability and Controllability of Differential Equations #math.AP #msc:37L55

paper · pdf · doi:10.48550/arxiv.0810.1988

arxiv created 2008/10/11 · arxiv updated 2009/12/01

Abstract

The existence of a random attractor in H¹(R³) × L²(R³) is proved for the damped semilinear stochastic wave equation defined on the entire space R³. The nonlinearity is allowed to have a cubic growth rate which is referred to as the critical exponent. The uniform pullback estimates on the tails of solutions for large space variables are established. The pullback asymptotic compactness of the random dynamical system is proved by using these tail estimates and the energy equation method.

Cited by

• Pullback Attractors for Non-autonomous Reaction-Diffusion Equations on Rⁿ

Related

• Random Attractor for Stochastic Wave Equation with Arbitrary Exponent and Additive Noise on ℝⁿ
• Multivalued Non-Autonomous Random Dynamical Systems for Wave Equations without Uniqueness
• Deterministic and random attractors for a wave equation with sign changing damping
• Random data Cauchy theory for nonlinear wave equations of power-type on ℝ³
• On the almost sure global well-posedness of energy sub-critical nonlinear wave equations on ℝ³