Life–span of classocal solutions to fully nonlinear wave equations

1991 ◽  
Vol 16 (6-7) ◽  
pp. 909-940 ◽  
Author(s):  
Ta-tsien Li ◽  
Li (Da-qian) ◽  
Yu Xin
Keyword(s):  
Life Span ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Nonlinear Wave Equations ◽  
Fully Nonlinear

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)).

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