Asymptotic Behavior of the Solution to the Cauchy Problemfor a Nonlinear Equation

Sufficient conditions are found for the existence and exponential decay of a global solution to the Cauchy problem for a nonlinear partial differential equation generalizing a damped sixth-order Boussinesq equation with double dispersion and the equation of transverse oscillations of a viscoelastic Voigt–Kelvin beam under the action of external and internal friction whose deformation is considered taking into account the correction for the inertia of section rotation.