scholarly journals ENERGY DECAY RATES FOR THE KIRCHHOFF TYPE WAVE EQUATION WITH BALAKRISHNAN-TAYLOR DAMPING AND ACOUSTIC BOUNDARY

2014 ◽  
Vol 30 (3) ◽  
pp. 249-258 ◽  
Author(s):  
Yong Han Kang
Keyword(s):  
Wave Equation ◽  
Energy Decay ◽  
Decay Rates ◽  
Kirchhoff Type ◽  
Type Wave ◽  
Energy Decay Rates

scholarly journals Global Existence and Energy Decay Rates for a Kirchhoff-Type Wave Equation with Nonlinear Dissipation

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Daewook Kim ◽  
Dojin Kim ◽  
Keum-Shik Hong ◽  
Il Hyo Jung
Keyword(s):  
Wave Equation ◽  
Existence And Uniqueness ◽  
Global Solutions ◽  
Growth Conditions ◽  
Decay Rates ◽  
Decay Estimates ◽  
Nonlinear Dissipation ◽  
Kirchhoff Type ◽  
Type Wave ◽  
Energy Decay Rates

The first objective of this paper is to prove the existence and uniqueness of global solutions for a Kirchhoff-type wave equation with nonlinear dissipation of the form under suitable assumptions on . Next, we derive decay estimates of the energy under some growth conditions on the nonlinear dissipationg. Lastly, numerical simulations in order to verify the analytical results are given.

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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