Homogenization of nonlinear hyperbolic problem with a dynamical boundary condition

Abstract

In this work, we look at homogenization results for nonlinear hyperbolic problem with a non-local boundary condition. We use the periodic unfolding method to obtain a homogenized nonlinear hyperbolic equation in a fixed domain. Due to the investigation's peculiarity, the unfolding technique must be developed with special attention, creating an unusual two-scale model. We note that the non-local boundary condition caused a damping on the homogenized model.

Keywords

• non-local interface condition
• nonlinear hyperbolic pdes
• homogenization
• the periodic unfolding method