General decay rate estimates for viscoelastic wave equation with Balakrishnan-Taylor damping (Q294019)

The author contributes to the amount of similar papers on a decay rate for viscoelastic wave equations. He considers the initial-boundary value problem \[ \begin{aligned} &u'' - M(t)\Delta u + \int_0^t h(t-\tau)\Delta u(\tau)\,d\tau+g(u')=f(u)\text{ in }\Omega\times (0,\infty),\\ &u=0\text{ on }\partial\Omega\times (0,\infty),\quad u(x,0)=u_0,\quad u'(0)=u_1,\quad x\in \Omega. \end{aligned} \] The main result involves various uniform decay rates of the energy due to the behavior of the kernel \(h\) without imposing any restrictive growth assumptions on the damping term \(g\).