Locally Periodic Unfolding Method and Two-Scale Convergence on Surfaces of Locally Periodic Microstructures

In this paper we generalize the periodic unfolding method and the notion of twoscale convergence on surfaces of periodic microstructures to locally periodic situations. The methods that we introduce allow us to consider a wide range of nonperiodic microstructures, especially to derive macroscopic equations for problems posed in domains with perforations distributed nonperiodically. Using the methods of locally periodic two-scale convergence on oscillating surfaces and the locally periodic boundary unfolding operator, we are able to analyze differential equations defined on boundaries of nonperiodic microstructures and consider nonhomogeneous Neumann conditions on the boundaries of perforations, distributed nonperiodically.