Rational Spectral Approximation Of Semilinear Strong Damped Wave Equation In Unbounded Domain A Matter Of Time

Recently, great developments had been made on the infinite dimensional dynamical systems. Mostly, more attentions are paid to the equations' numerical simulations , for their exact solution can't be gotten.As an important numerical method, spectral method has infinite convergence. So using spectral method to discuss infinite dimensional dynamical systems aroused many attentions.This work focuses on the study of wave equation on the whole space. Its main purpose is to investigate the long-time behaviors of rational spectral approximation to strongly damped semi-linear wave equation on the whole space. We construct semi- discrete and fully discrete rational spectral scheme and priori estimates. At same time we discuss their error estimate,the existence of approximate attractors A_N and the upper semi-continuity on A which is a global attractor of initial problem.