scholarly journals Global existence and asymptotic behaviour of solutions for a class of fourth order strongly damped nonlinear wave equations

2012 ◽  
Vol 71 (3) ◽  
pp. 401-415 ◽  
Author(s):  
Xu Runzhang ◽  
Yang Yanbing
Keyword(s):  
Global Existence ◽  
Asymptotic Behaviour ◽  
Nonlinear Wave ◽  
Fourth Order ◽  
Wave Equations ◽  
Nonlinear Wave Equations ◽  
Asymptotic Behaviour Of Solutions ◽  
Strongly Damped

scholarly journals Global Existence of Strong Solutions to a Class of Fully Nonlinear Wave Equations with Strongly Damped Terms

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Zhigang Pan ◽  
Hong Luo ◽  
Tian Ma
Keyword(s):  
Global Existence ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Galerkin Approximation ◽  
Strong Solutions ◽  
Nonlinear Wave Equations ◽  
Existence Of A Solution ◽  
Fully Nonlinear ◽  
Sequence Techniques ◽  
Strongly Damped

We consider the global existence of strong solutionu, corresponding to a class of fully nonlinear wave equations with strongly damped termsutt-kΔut=f(x,Δu)+g(x,u,Du,D2u)in a bounded and smooth domainΩinRn, wheref(x,Δu)is a given monotone inΔunonlinearity satisfying some dissipativity and growth restrictions andg(x,u,Du,D2u)is in a sense subordinated tof(x,Δu). By using spatial sequence techniques, the Galerkin approximation method, and some monotonicity arguments, we obtained the global existence of a solutionu∈Lloc∞((0,∞),W2,p(Ω)∩W01,p(Ω)).

scholarly journals Global well-posedness of a class of fourth-order strongly damped nonlinear wave equations

2019 ◽  
Vol 39 (2) ◽  
pp. 297
Author(s):  
Yang Yanbing ◽  
Md Salik Ahmed ◽  
Qin Lanlan ◽  
Xu Runzhang
Keyword(s):  
Nonlinear Wave ◽  
Fourth Order ◽  
Wave Equations ◽  
Nonlinear Wave Equations ◽  
Well Posedness ◽  
Strongly Damped

scholarly journals Global existence and decay estimates for nonlinear wave equations with space-time dependent dissipative term

2015 ◽  
Vol 12 (02) ◽  
pp. 249-276
Author(s):  
Tomonari Watanabe
Keyword(s):  
Global Existence ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Space Time ◽  
Time Dependent ◽  
Nonlinear Wave Equations ◽  
Energy Estimates ◽  
Space Region ◽  
Decay Estimates ◽  
Dissipative Term

We study the global existence and the derivation of decay estimates for nonlinear wave equations with a space-time dependent dissipative term posed in an exterior domain. The linear dissipative effect may vanish in a compact space region and, moreover, the nonlinear terms need not be in a divergence form. In order to establish higher-order energy estimates, we introduce an argument based on a suitable rescaling. The proposed method is useful to control certain derivatives of the dissipation coefficient.

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