Global Solution, Decay, and Blow-Up of a Viscoelastic Kirchhoff System with Logarithmic Nonlinearity and Acoustic Fractional Delay Boundary Conditions

We examine a nonlinear viscoelastic Kirchhoff model endowed with a logarithmic source. Assuming suitable hypotheses and under the inclusion of nonlinear distributed delay feedback terms, in addition to the acoustic and fractional boundary feedback terms, we obtain global existence, general decay estimates, and finite-time blow-up for negative initial energy, all for a wide range of relaxation kernels. The Kirchhoff term K(∥∇W∥22) significantly changes the structure of the Nehari manifold and requires a new energy functional based on the primitive K^. Our analysis identifies the precise blow-up mechanism and establishes sharp dimension-dependent restrictions on the exponent p. Our outcomes broaden and enhance recent contributions on classical wave equations to the physically meaningful Kirchhoff framework.