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Energy decay for the wave equation with a degenerate dissipative term

Published online by Cambridge University Press:  14 November 2011

Mitsuhiro Nakao
Mitsuhiro Nakao
Affiliation:
Department of Mathematics, College of General Education, Kyushu University, Fukuoka 810, Japan
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Synopsis

Decay estimates for the energy are derived for the initial boundary value problem of the wave equation with a degenerate dissipative term:

where Ω is a bounded domain in Rn, a(×) is a nonnegative function such that a1 ∊Lp(Ω) for some p > 0 and f is a function tending to 0 rapidly as t → ∞

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 100 , Issue 1-2 , 1985 , pp. 19 - 27
Copyright
Copyright © Royal Society of Edinburgh 1985

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References

1Dafermos, C.. Asymptotic behaviour of solutions of evolution equations. In Nonlinear Evolution Equations, ed. Crandall, M. G. (New York: Academic Press, 1978).Google Scholar
2Ikawa, M.. Mixed problems for hyperbolic equations of second order. J. Math. Soc. Japan 20 (1968), 580–608.Google Scholar
3Nakao, M.. A difference inequality and its application to nonlinear evolution equations. J. Math. Soc. Japan 30 (1978), 747–762.CrossRefGoogle Scholar
4Rauch, J.. Qualitative behavior of dissipative wave equations on bounded domains. Arch. Rational Mech. Anal. 62 (1976), 77–85.CrossRefGoogle Scholar
5Redheffer, R. and Walter, W.. A comparison theorem for difference inqualities. J. Differential Equations 44 (1982), 111–117.CrossRefGoogle Scholar
6Russell, D. L.. Decay rates for weakly damped systems in Hilbert space. J. Differential Equations 19 (1975), 334–370.Google Scholar
7Strauss, W. A.. The Energy Method in Nonlinear Partial Differential Equations. Notas Mat 17 (1969).Google Scholar