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Decay estimates of solutions for the wave equations with strong damping terms in unbounded domains
Author(s) -
Ikehata Ryo
Publication year - 2001
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.235
Subject(s) - mathematics , dissipation , argument (complex analysis) , domain (mathematical analysis) , wave equation , energy (signal processing) , mathematical analysis , inequality , energy method , calculus (dental) , statistics , physics , quantum mechanics , medicine , biochemistry , chemistry , dentistry
Abstract This paper is concerned with some uniform energy decay estimates of solutions to the linear wave equations with strong dissipation in the exterior domain case. We shall derive the decay rate such as $(1+t)E(t)\le C$\nopagenumbers\end for some kinds of weighted initial data, where E ( t ) represents the total energy. Our method is based on the combination of the argument due to Ikehata–Matsuyama with the Hardy inequality, which is an improvement of Morawetz method. Copyright © 2001 John Wiley & Sons, Ltd.