On exponential observability estimates for the heat semigroup with explicit rates - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Rendiconti Lincei. Matematica e Applicazioni Année : 2006

On exponential observability estimates for the heat semigroup with explicit rates

Résumé

This note concerns the final time observability inequality from an interior region for the heat semigroup, which is equivalent to the null-controllability of the heat equation by a square integrable source supported in this region. It focuses on exponential estimates in short times of the observability cost, also known as the control cost and the minimal energy function. It proves that this final time observability inequality implies four variants (an integrated inequality with singular weights, an integrated inequality in infinite times, a sharper inequality and a Sobolev inequality) with roughly the same exponential rate everywhere and some control cost estimates with explicit exponential rates concerning null-controllability, null-reachability and approximate controllability. A conjecture and open problems about the optimal rate are stated. This note also contains a brief review of recent or to be published papers related to exponential observability estimates: boundary observability, Schrödinger group, anomalous diffusion, thermoelastic plates, plates with square root damping and other elastic systems with structural damping.
Fichier principal
Vignette du fichier
Miller.ExpObsHeat.HAL.140506.pdf (262.44 Ko) Télécharger le fichier

Dates et versions

hal-00016070 , version 1 (16-12-2005)
hal-00016070 , version 2 (19-12-2005)
hal-00016070 , version 3 (30-01-2006)
hal-00016070 , version 4 (14-05-2006)

Identifiants

  • HAL Id : hal-00016070 , version 4

Citer

Luc Miller. On exponential observability estimates for the heat semigroup with explicit rates. Rendiconti Lincei. Matematica e Applicazioni, 2006, 17 (4), pp.351--366. ⟨hal-00016070v4⟩
250 Consultations
260 Téléchargements

Partager

Gmail Facebook X LinkedIn More