Energy decay rates for solutions of the wave equation with boundary damping and source term

2009 ◽  
Vol 61 (2) ◽  
pp. 235-265 ◽  
Author(s):  
Jong Yeoul Park ◽  
Tae Gab Ha ◽  
Yong Han Kang
Keyword(s):  
Wave Equation ◽  
Source Term ◽  
Energy Decay ◽  
Decay Rates ◽  
Boundary Damping ◽  
Energy Decay Rates

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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