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Sharp energy decay estimates for the wave equation with a local degenerate dissipation

โœ Scribed by Yong Han Kang; Mi Jin Lee; Il Hyo Jung

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
445 KB
Volume
57
Category
Article
ISSN
0898-1221

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โœฆ Synopsis

We derive a fast decay estimate for the wave equation with a local degenerate dissipation of the type a(x)u t in a bounded domain โ„ฆ. The dissipative coefficient a(x) is a nonnegative function only on a neighborhood of some part of the boundary โˆ‚โ„ฆ and may vanish somewhere in โ„ฆ. The results obtained extend and improve on earlier results of Nakao as well as those of Tcheugouรฉ Tรฉbou. The method of proof is based on multipliers technique and some modified interpolation and difference inequalities.

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