A spectral inequality for degenerated operators and applications

TL;DR

This paper proves a spectral inequality for degenerated elliptic operators and demonstrates its applications in impulse control and finite-time stabilization of degenerated parabolic equations.

Contribution

It establishes a Lebeau-Robbiano spectral inequality for degenerated operators and applies it to control and stabilization problems.

Findings

Spectral inequality for degenerated elliptic operators proven.

Application to impulse control of degenerated parabolic equations.

Application to finite-time stabilization of degenerated parabolic equations.

Abstract

In this paper we establish a Lebeau-Robbiano spectral inequality for a degenerated one dimensional elliptic operator and show how it can be used to impulse control and finite time stabilization for a degenerated parabolic equation. R{\'e}sum{\'e} .-Dans cet article, on s'int{\'e}r{\`e}ss{\`e} a l'in{\'e}galit{\'e} spectrale de type Lebeau-Robbiano sur la somme de fonctions propres pour une famille d'op{\'e}rateurs d{\'e}g{\'e}n{\'e}r{\'e}s. Les applications sont donn{\'e}es en th{\'e}orie du contr{\^o}le comme le contr{\^o}le impulsionnel et la stabilisation en temps fini.