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Asymptotic stability of webster-Lokshin equation

Matignon, Denis and Prieur, Christophe Asymptotic stability of webster-Lokshin equation. (2014) Mathematical Control and Related Fields (MCRF), 4 (4). 481-500. ISSN 2156-8472

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Official URL: http://dx.doi.org/10.3934/mcrf.2014.4.481


The Webster-Lokshin equation is a partial differential equation is considered in this paper. It models the sound velocity in an acoustic domain. The dynamics contains linear fractional derivatives which can admits a infinite dimensional representation of diffusive type. The boundary conditions are described by impedance condition which can be represented by two finite dimensional systems. Under the physical assumptions, there is a natural energy inequality. However, due to a lack of precompactness of the solutions, LaSalle's invariance principle can not be applied. The asymptotic stability of the system is proved by studying the resolvent equation, and by using the Arendt-Batty stability condition.

Item Type:Article
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Other partners > Institut polytechnique de Grenoble (FRANCE)
Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
Other partners > Université Joseph Fourier Grenoble 1 - UJF (FRANCE)
Other partners > Université Stendhal-Grenoble 3 - U3 (FRANCE)
Laboratory name:
Deposited On:18 Oct 2013 10:03

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