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ABSTRACT
The initial-boundary value problem of logarithmic viscoelastic wave equation in three space dimensions is studied. The existence of local and global solutions for this problem are proved by means of the contraction mapping criterion and potential well method. Meanwhile, the blow-up of solutions in the unstable set is also obtained.
Disclosure statement
No potential conflict of interest was reported by the author.
Additional information
Funding
This research was supported by Natural Science Foundation of Zhejiang Province [grant number LY17A010009] and the National Natural Science Foundation of China [grant number 61273016].