Decay Estimates for the Wave Equation with Internal Damping

1994 ◽  
pp. 253-266 ◽  
Author(s):  
Vilmos Komornik
Keyword(s):  
Wave Equation ◽  
Decay Estimates ◽  
Internal Damping

scholarly journals Global existence and dynamic structure of solutions for damped wave equation involving the fractional Laplacian

2021 ◽  
Vol 54 (1) ◽  
pp. 245-258
Author(s):  
Younes Bidi ◽  
Abderrahmane Beniani ◽  
Khaled Zennir ◽  
Ahmed Himadan
Keyword(s):  
Wave Equation ◽  
Global Solution ◽  
Fractional Laplacian ◽  
Necessary Conditions ◽  
Dynamic Structure ◽  
Decay Estimates ◽  
Damped Wave Equation ◽  
Structure Of Solutions ◽  
Nonlinear Source ◽  
Galerkin Approximations

Abstract We consider strong damped wave equation involving the fractional Laplacian with nonlinear source. The results of global solution under necessary conditions on the critical exponent are established. The existence is proved by using the Galerkin approximations combined with the potential well theory. Moreover, we showed new decay estimates of global solution.

scholarly journals Sharp energy decay estimates for the wave equation with a local degenerate dissipation

2009 ◽  
Vol 57 (1) ◽  
pp. 21-27 ◽  
Author(s):  
Yong Han Kang ◽  
Mi Jin Lee ◽  
Il Hyo Jung
Keyword(s):  
Wave Equation ◽  
Energy Decay ◽  
Decay Estimates

scholarly journals Decay estimates for the wave equation in two dimensions

2016 ◽  
Vol 260 (6) ◽  
pp. 5378-5420 ◽  
Author(s):  
Marius Beceanu
Keyword(s):  
Wave Equation ◽  
Two Dimensions ◽  
Decay Estimates

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.

Sign in / Sign up

Export Citation Format

Share Document