Nonlinear Neumann boundary stabilization of the wave equation using rotated multipliers

TL;DR

This paper introduces a rotated multipliers method for stabilizing the wave equation with nonlinear Neumann boundary feedback, expanding geometric conditions for boundary control and addressing singularities caused by mixed boundary conditions.

Contribution

It develops a new geometric framework for boundary stabilization of the wave equation using rotated multipliers, handling nonlinear feedback and boundary singularities.

Findings

Achieves stabilization under specific geometric conditions.

Handles nonlinear Neumann boundary feedback.

Addresses boundary singularities due to mixed conditions.

Abstract

The rotated multipliers method is performed in the case of the boundary stabilization by means of a(linear or non-linear) Neumann feedback. this method leads to new geometrical cases concerning the "active" part of the boundary where the feedback is apllied. Due to mixed boundary conditions, these cases generate singularities. Under a simple geometrical conditon concerning the orientation of boundary, we obtain a stabilization result in both cases.