On the optimality of the observability inequalities for parabolic and hyperbolic systems with potentials

Duyckaerts T, Zhang X, Zuazua E (2008)

Publication Type: Journal article

Publication year: 2008

Journal

Annales de l'Institut Henri Poincaré - Analyse Non Linéaire Elsevier Masson / Institute Henri Poincaré

Book Volume: 25

Pages Range: 1-41

Journal Issue: 1

DOI: 10.1016/j.anihpc.2006.07.005

Abstract

In this paper we prove the optimality of the observability inequality for parabolic systems with potentials in even space dimensions n >= 2. This inequality (derived by E. FernAndez-Cara and the third author in the context of the scalar heat equation with potentials in any space dimension) asserts, roughly, that for small time, the total energy of solutions can be estimated from above in terms of the energy localized in a subdomain with an observability constant of the order of exp(C parallel to a parallel to(2/3)(infinity)), a being the potential involved in the system. The problem of the optimality of the observability inequality remains open for scalar equations.

Authors with CRIS profile

Enrique Zuazua Iriondo

Involved external institutions

Academia Sinica / 中央研究院 TW Taiwan (TW) Universidad Autónoma de Madrid (UAM) ES Spain (ES) Université de Cergy-Pontoise FR France (FR)

How to cite

APA:

Duyckaerts, T., Zhang, X., & Zuazua, E. (2008). On the optimality of the observability inequalities for parabolic and hyperbolic systems with potentials. Annales de l'Institut Henri Poincaré - Analyse Non Linéaire, 25(1), 1-41. https://dx.doi.org/10.1016/j.anihpc.2006.07.005

MLA:

Duyckaerts, Thomas, Xu Zhang, and Enrique Zuazua. "On the optimality of the observability inequalities for parabolic and hyperbolic systems with potentials." Annales de l'Institut Henri Poincaré - Analyse Non Linéaire 25.1 (2008): 1-41.

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