Some generalized results for global well-poseness for wave equations with damping and source terms

Runzhang Xu and Jihong Shen

Mathematics and Computers in Simulation (MATCOM), 2009, vol. 80, issue 4, 804-807

Abstract: In this paper we study the initial boundary value problem of wave equations with nonlinear damping and source terms:utt−Δu+a|ut|m−1ut=b|u|p−1u,x∈Ω,t>0,u(x,0)=u0(x),ut(x,0)=u1(x),x∈Ω,u(x,t)=0,x∈∂Ω,t≥0,where Ω⊂RN is a suitably smooth bounded domain. We prove that for any a>0 and b>0, if 10, above problem admits a global solution u(x,t)∈L∞(0,T;H01(Ω)∩Lp+1(Ω)) with ut(x,t)∈L∞(0,T;L2(Ω))∩Lm+1(Ω×[0,T]). So the results of Georgiev and Ikehata are generalized and improved.

Keywords: Wave equation; Nonlinear damping; Global solutions; Existence (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:80:y:2009:i:4:p:804-807

DOI: 10.1016/j.matcom.2009.08.026

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