HOMOGENIZATION WITH MULTIPLE SCALE EXPANSION ON SELFSIMILAR STRUCTURES

Abstract. The homogenization theory is devoted to analysis of partial differential equations with rapidly oscillating coefficients. Let Ak be a given partial differential operator and we consider the equation Akuk = f, together with the appropriate boundary initial conditions. Here k ∈ N and f ∈ H1(Rn). We are interested in studying the solutions of this system in the limit as k →∞. The homogenization theory is devoted to analysis of partial differential equa-tions with rapidly oscillating coefficients. Let A be a given partial differential oper-ator and we consider the equation Au = f, together with the appropriate boundary initial conditions. Here is a small parameter << 1, associated with the oscillations. We are interested in studying the solutions of this system in the limit as → 0. The homogenization theory study the following issues: • Convergence to a limit. • Characterization of the limiting process. Au = f • Explicit analytical construction of A