  In the present work we shall describe and apply the techniques of the
Renormalization Group - based in data rescaling and operator renormalizing -
and of Homogenization - that substitutes, in a certain limit, a periodically
inhomogeneous medium by a homogeneous one - for the study of asymptotic
behavior of solutions of PDE's.
  One class of problems studied in this dissertation consists of nonlinear,
diffusive differential equations with periodic coefficients, that supposedly
model the diffusion in a heterogeneous medium. Our study of these problems
involves arguments originated from the two techniques described above. This
makes, in certain sense, a connection between both of them.
  Another class of problems studied here consists of nonlinear, diffusive
equations with time dependent coefficients, originated from montecarlo
simulation of the asymptotic behavior of the averaged solutions of stochastic
differential equations modeling the phenomenon of two-phase flow in porous
media.
  Using the Renormalization Group we shall classify the problems in accordance
with their qualitative behavior. This classification will be verified
numerically. We shall also study the curve of phase transition that separates
asymptotic regimes predominantly linear and nonlinear. The main results
presented in this work are given by a numerical version of the Renormalization
Group, which will be described in detail in the body of this dissertation.
