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Exponential Energy Decay Estimate for the Solutions of Internally Damped Wave Equation in a Bounded Domain

✍ Scribed by Ganesh C Gorain

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
175 KB
Volume
216
Category
Article
ISSN
0022-247X

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✦ Synopsis

Here we are concerned about the stability of the solution of internally damped wave equation y Y s ⌬ y q ⌬ y X with small damping constant ) 0, in a bounded domain ⍀ in R n under mixed undamped boundary conditions. A uniform expo-Ε½ . y␀ t Ε½ . nential energy decay rate E t F Me E 0 where M G 1 and ␀ s r , 0 0 being a quadratic function of , is proved for the solution of this type of boundary value problem. Earlier authors have considered the undamped wave equation with certain forms of damped boundary conditions proving similar and faster energy decay rates.

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## 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__(