We investigate the initial-boundary value problem for a viscoelastic Petrovsky system of Kirchhoff-type with nonlinear source term. By applying the standard continuation principle, the existence of global solutions for this problem is proved and the exponential decay estimate of global solutions is obtained.
"Global existence and exponential decay for a viscoelastic Petrovsky system." Rocky Mountain J. Math. 49 (5) 1709 - 1724, 2019. https://doi.org/10.1216/RMJ-2019-49-5-1709