Blow-up and global existence analysis for the viscoelastic wave equation with a frictional and a Kelvin-Voigt damping
Summary: We are concerned in this paper with the initial boundary value problem for a quasilinear viscoelastic wave equation which is subject to a nonlinear action, to a nonlinear frictional damping, and to a Kelvin-Voigt damping, simultaneously. By utilizing a carefully chosen Lyapunov functional, we establish first by the celebrated convexity argument a finite time blow-up criterion for the initial boundary value problem in question; we prove second by an a priori estimate argument that some solutions to the problem exists globally if the nonlinearity is ``weaker,'' in a certain sense, than the frictional damping, and if the viscoelastic damping is sufficiently strong.
scientific article; zbMATH DE number 6992036
scientific article