Energy Decay Estimates of Solutions for Viscoelastic Damped Wave Equations in $$\mathbf {R}^{n}$$

Abstract

In the present work, we investigate the global existence and uniform decay rates of solutions to the Cauchy problem in $$\mathbf {R}^{n}$$ ( $$n\ge 1)$$ related to the dynamic behavior of evolution equations accounting for rotational inertial forces along with a linear viscoelastic memory damping arising in viscoelastic materials. Under certain conditions on the initial data and on the kernel, the global existence and decay estimates of the solutions are established. Furthermore, time decay estimates in higher Sobolev space of the solution are provided. The proof is carried out by means of the point-wise decay estimates of the solution in the Fourier space.