Periodic D-Pullback Attractor of Strongly Damped Sine-Gordon Equation with Memory
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LV Penghui, LIN Guoguang, LV Xiaojun
We study the existence of periodic pullback attractor for non-autonomous dynamical system generated by Sine-Gordon equation with non-autonomous term as well as memory. By a priori estimation, we obtain the global solution of the equation and the pullback absorting set of ; by constructing the contraction function, we prove the asymptotic compactness of , then the existence of pullback attractor of the corresponding non-autonomous dynamical system in is established; moreover the pullback attractor is proved to be periodic, when the non-autonomous dynamical system has a periodic deterministic forcing term.
Sine-gordon equation, History memory, Pullback d-asymptotic compactness, Periodic pullback attractor