On the stabilization of the elasticity system by the boundary

TL;DR

This paper investigates how to stabilize the elasticity system outside a convex body by using boundary conditions that dissipate energy, identifying conditions that prevent resonance phenomena.

Contribution

It establishes resonance-free regions for the elasticity system with dissipative boundary conditions on convex bodies, under natural geometric assumptions.

Findings

Resonance-free regions are characterized for the elasticity system.

Dissipative boundary conditions effectively prevent resonances.

Results depend on the geometry of the boundary and geodesic behavior.

Abstract

We obtain free of resonances regions for the elasticity system in the exterior of a strictly convex body with dissipative boundary conditions under some natural assumptions on the behaviour of the geodesics on the boundary.