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Polynomial stabiization of the wave equation with Ventcel's boundary conditions
Author(s) -
Nicaise Serge,
Laoubi Karima
Publication year - 2010
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200710162
Subject(s) - mathematics , polynomial , mathematical analysis , boundary value problem , boundary (topology) , fourier transform , wave equation , square (algebra) , plane (geometry) , stability (learning theory) , geometry , machine learning , computer science
We consider the wave equation on the unit square of the plane with Ventcel boundary conditions on a part of the boundary. It was shown by A. Heminna [8] that this problem is not exponentially stable. Here using a Fourier analysis and a careful analysis of the 1‐d problem with respect to the Fourier parameter l , we show a polynomial stability of this system (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)