General Decay for a Viscoelastic Equation with Acoustic Boundary Conditions and a Logarithmic Nonlinearity

In this work, we investigate the stability of solutions in a situation where the logarithmic source term competes with the viscoelastic dissipation under acoustic boundary conditions. We assume minimal conditions on the relaxation function g, namely, g′(t)≤−ξ(t)H(g(t)), where H is a strictly increasing and strictly convex function near the origin, and ξ(t) is a non-increasing function. Under these general assumptions, we establish a general decay estimate for the solution. This result extends and improves some previous results.