Abstract: We considered  the decay rate of solutions to a class of nonlocal wave equations with  Kirchhoff term. Firstly, by establishing weighted estimates of the Sobolev norm, the difficulty of classical multiplier method failure caused by  supercritical damping term could be overcome. Secondly, by using  the weighted multiplier method to prove that the energy functional of the studied  problem decayed  logarithmically when  the damping term was supercritical damping,  which was  totally different from both exponential decay of linear damping and polynomial decay of subcritical damping.

Key words: nonlocal equation, weighted multiplier method, decay estimate