  In this work we use functional methods to prove the boundedness and global
existence of solutions for a class of strongly coupled parabolic systems. We
apply the results to deduce the global existence of solutions for a classic
Shigesada-Kawasaki-Teramoto (SKT) type model, for an extended range of the
self-diffusion and cross-diffusion coefficients than those available in the
current literature. We provide numerical simulations in 2D, via a spectral
Galerkin method to verify our global existence results, as well as to visualize
the dynamics of the system.
