We consider the total energy decay of the Cauchy problem for wave equations with a potential and an effective damping. We treat it in the whole one-dimensional Euclidean space [Formula: see text]. Fast energy decay like [Formula: see text] is established with the help of potential. The proofs of main results rely on a multiplier method and modified techniques adopted in [R. Ikehata and Y. Inoue, Total energy decay for semilinear wave equations with a critical potential type of damping, Nonlinear Anal. 69(4) (2008) 1396–1401].
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Li et al. (2024) studied this question.
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