On a nonlinear hyperbolic equation with anisotropy: Global existence and decay of solution

We establish the existence of a global solution to an initial boundary value problem for the nonlinear anisotropic hyperbolic equation u″−∑i=1n∂∂xi(|∂u∂xi|pi−2∂u∂xi)−Δu′+g(x,u)=f(x,t). Depending on the range of the pipi’s, we derive an exponential and a polynomial decay for the global solution.