EXISTENCE OF GLOBAL SOLUTIONS FOR THE KIRCHHOFF-TYPE QUASILINEAR WAVE EQUATION IN EXTERIOR DOMAINS WITH A HALF-LINEAR DISSIPATION

2004 ◽  
Vol 58 (2) ◽  
pp. 373-391 ◽  
Author(s):  
Mitsuhiro NAKAO
Keyword(s):  
Wave Equation ◽  
Global Solutions ◽  
Exterior Domains ◽  
Quasilinear Wave Equation ◽  
Kirchhoff Type

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.

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