Long time averaged reflection force and homogenization of oscillating Neumann boundary conditions

TL;DR

This paper investigates the existence of an ergodic number in oblique boundary conditions and applies this concept to homogenize oscillating Neumann boundary conditions.

Contribution

It establishes the existence and uniqueness of the ergodic number and demonstrates its application in homogenization of oscillating Neumann boundary conditions.

Findings

Existence and uniqueness of the ergodic number d.

Application of d to homogenization of oscillating Neumann conditions.

Insights into long-term averaged reflection forces.

Abstract

This paper concerns with two issues. The first issue is the existence and the uniqueness of the ergodic type number $d$ which appears in the oblique boundary condition. The second issue is the application of the number for the study of homogenizations of oscillating Neumann boundary conditions.