PULLBACK AND FORWARD ATTRACTORS FOR A DAMPED WAVE EQUATION WITH DELAYS

2004/08/30 by T. CARABALLO, Tomás Caraballo, Peter E. Kloeden +3 · 2 citations
Engineering · Mathematics · Computer Science · #Stability and Controllability of Differential Equations #Advanced Mathematical Physics Problems #Advanced Mathematical Modeling in Engineering

paper · doi:10.1142/s0219493704001139

Abstract

The existence of a pullback (and also a uniform forward) attractor is proved for a damped wave equation containing a delay forcing term which, in particular, covers the models of sine–Gordon type. The result follows from the existence of a compact set which is uniformly attracting for the two-parameter semigroup associated to the model.

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• Stochastic delay differential equations with jumps in differentiable\n manifolds
• One-dimensional random attractor and rotation number of the stochastic damped sine-Gordon equation

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