Asymptotic Behavior for a Viscoelastic Wave Equation With Acoustic and Fractional Conditions Combined by Nonlinear Time‐Varying Delay in Boundary Feedback in the Presence of Logarithmic Source Term

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ABSTRACTThis study examines a wave equation within the framework of nonlinear viscoelasticity. Specifically, it considers a nonlinear, time‐varying delay feedback acting on the boundary, coupled with acoustic and fractional boundary conditions, and influenced by a logarithmic source term. Under suitable general assumptions on the kernel, we first establish the global existence of solutions and subsequently analyze their asymptotic behavior.