Energy decay rates for the semilinear wave equation with nonlinear localized damping and source terms

2006 ◽  
Vol 64 (8) ◽  
pp. 1757-1797 ◽  
Author(s):  
Irena Lasiecka ◽  
Daniel Toundykov
Keyword(s):  
Wave Equation ◽  
Energy Decay ◽  
Decay Rates ◽  
Source Terms ◽  
Semilinear Wave Equation ◽  
Energy Decay Rates ◽  
Localized Damping ◽  
Damping And Source Terms

Asymptotic stability and energy decay rates for solutions of hyperbolic equations with boundary damping

1977 ◽  
Vol 77 (1-2) ◽  
pp. 97-127 ◽  
Author(s):  
John P. Quinn ◽  
David L. Russell
Keyword(s):  
Wave Equation ◽  
Asymptotic Stability ◽  
Asymptotic Behaviour ◽  
Hyperbolic Equations ◽  
Energy Decay ◽  
Decay Rates ◽  
The Other ◽  
Boundary Damping ◽  
Energy Absorbing ◽  
Energy Decay Rates

SynopsisThis report deals with the asymptotic behaviour of solutions of the wave equation in a domain Ω ⊆Rn. The boundary, Γof Ωft consists of two parts. One part reflects all energy while the other part absorbs energy to a degree. If the energy-absorbing part is non-empty we show that the energy tends to zero as t→∞. With stronger assumptions we are able to obtain decay rates for the energy. Certain relationships with controlability are discussed and used to advantage.

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