Global existence and uniform decay of solutions for a system of wave equations with dispersive and dissipative terms

2010 ◽  
Vol 5 (3) ◽  
pp. 555-574 ◽  
Author(s):  
Wenjun Liu
Keyword(s):  
Global Existence ◽  
Wave Equations ◽  
Uniform Decay ◽  
Decay Of Solutions ◽  
Dissipative Terms

scholarly journals Global existence of solutions to degenerate wave equations with dissipative terms

1999 ◽  
Vol 60 (1) ◽  
pp. 1-10
Author(s):  
Mohammed Aassila
Keyword(s):  
Wave Equation ◽  
Global Existence ◽  
Asymptotic Behaviour ◽  
Wave Equations ◽  
Existence Of Solutions ◽  
Dissipative Term ◽  
Global Existence Of Solutions ◽  
Asymptotic Behaviour Of Solutions ◽  
Dissipative Terms ◽  
Degenerate Wave Equation

In this paper we prove the global existence and study the asymptotic behaviour of solutions to a degenerate wave equation with a nonlinear dissipative term.

scholarly journals Existence and uniform decay of solutions for a class of generalized plate-membrane-like systems

2006 ◽  
Vol 2006 ◽  
pp. 1-24
Author(s):  
Haihong Liu ◽  
Ning Su
Keyword(s):  
Asymptotic Behavior ◽  
Global Existence ◽  
Nonlinear Damping ◽  
Asymptotic Behavior Of Solutions ◽  
Uniform Decay ◽  
Decay Of Solutions

We study the global existence, uniqueness, and asymptotic behavior of solutions for a class of generalized plate-membrane-like systems with nonlinear damping and source acting both interior and on boundary.

Remarks on nonlinear elastic waves with null conditions

2020 ◽  
Vol 26 ◽  
pp. 121
Author(s):  
Dongbing Zha ◽  
Weimin Peng
Keyword(s):  
Initial Data ◽  
Global Existence ◽  
Elastic Waves ◽  
Wave Equations ◽  
Alternative Proof ◽  
Classical Solutions ◽  
Small Initial Data ◽  
Hyperelastic Materials ◽  
Variational Structure ◽  
Nonlinear Elastic

For the Cauchy problem of nonlinear elastic wave equations for 3D isotropic, homogeneous and hyperelastic materials with null conditions, global existence of classical solutions with small initial data was proved in R. Agemi (Invent. Math. 142 (2000) 225–250) and T. C. Sideris (Ann. Math. 151 (2000) 849–874) independently. In this paper, we will give some remarks and an alternative proof for it. First, we give the explicit variational structure of nonlinear elastic waves. Thus we can identify whether materials satisfy the null condition by checking the stored energy function directly. Furthermore, by some careful analyses on the nonlinear structure, we show that the Helmholtz projection, which is usually considered to be ill-suited for nonlinear analysis, can be in fact used to show the global existence result. We also improve the amount of Sobolev regularity of initial data, which seems optimal in the framework of classical solutions.

scholarly journals Global existence of null-form wave equations in exterior domains

2007 ◽  
Vol 256 (3) ◽  
pp. 521-549 ◽  
Author(s):  
Jason Metcalfe ◽  
Christopher D. Sogge
Keyword(s):  
Global Existence ◽  
Wave Equations ◽  
Exterior Domains
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