The Energy Decay Problem for Wave Equations with Nonlinear Dissipative Terms in ℝn

We study the asymptotic behavior of energy for wave equations with nonlinear damping g(ut) = |ut|m–1ut in ℝn (n ≥ 3) as time t → ∞. The main result shows a polynomial decay rate of energy under the condition 1 < m ≤ (n + 2)/(n + 1). Previously, only logarithmic decay rates were found.

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Bibliographic Details
Published in:Indiana University mathematics journal 2007-01, Vol.56 (1), p.389-416
Main Authors: Todorova, Grozdena, Yordanov, Borislav
Format: Article
Language:English
Subjects:
Damping
Differential equations
Exact sciences and technology
Harmonic analysis
Klein Gordon equation
Mathematical analysis
Mathematics
Partial differential equations
Polynomials
Preliminary estimates
Sciences and techniques of general use
Spacetime
Wave equations
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Description
Summary:We study the asymptotic behavior of energy for wave equations with nonlinear damping g(ut) = |ut|m–1ut in ℝn (n ≥ 3) as time t → ∞. The main result shows a polynomial decay rate of energy under the condition 1 < m ≤ (n + 2)/(n + 1). Previously, only logarithmic decay rates were found.
ISSN:0022-2518
1943-5258