Mathematical analysis demonstrates global existence, asymptotic stability, and finite-time blow-up in viscoelastic wave equations, highlighting energy thresholds that govern system stability.
This paper investigates a class of ‐Laplacian‐viscoelastic wave equations with logarithmic source terms, defined on a bounded domain . First, we prove the local existence of solutions by using the Faedo–Galerkin method. Next, by combining analytical techniques, including the potential well method and energy estimates, we establish the global existence of solutions. Furthermore, employing the Komornik inequality, we prove the asymptotic stability of these solutions. Finally, through an integration of the potential well framework with concavity arguments, we demonstrate the occurrence of blow‐up phenomena under conditions of positive initial energy and derive an upper bound for the blow‐up time.
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Shahrouzi et al. (2026) studied this question.
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