Improved decay of solution for strongly damped nonlinear wave equations

In this work, we deal with the initial boundary value problem of solutions for a class of linear strongly damped nonlinear wave equations u(tt) - Delta u - alpha Delta u(t) = f(u) in the frame of a family of potential wells. For this strongly damped wave equation, we not only prove the global-in-time existence of the solution, but we also improve the decay rate of the solution from the polynomial decay rate to the exponential decay rate.