Uniform Stabilization of the wave equation on compact surfaces and locally distributed damping

TL;DR

This paper investigates the stabilization of the wave equation on compact surfaces using locally distributed damping, focusing on cases where damping is effective outside visible umbilical sets, contributing to control theory on geometric surfaces.

Contribution

It introduces a novel stabilization method for wave equations on compact surfaces with damping effective outside visible umbilical sets, expanding control techniques in geometric contexts.

Findings

Stability achieved with damping outside umbilical sets

Effective damping leads to exponential decay of energy

Applicable to a broad class of compact surfaces

Abstract

This paper is concerned with the study of the wave equation on compact surfaces and locally distributed damping. We study the case where the damping is effective on the complement of visible umbilical sets.