Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
842151 | Nonlinear Analysis: Theory, Methods & Applications | 2008 | 12 Pages |
Abstract
In this paper, we consider the following problem utt−α△ut+△2u−△u=f(u),x∈Ω,t>0,u(x,0)=u0(x),ut(x,0)=u1(x),x∈Ω,△u(x,t)|∂Ω=u(x,t)|∂Ω=0,t≥0, where Ω⊂RnΩ⊂Rn is a bounded domain with smooth boundary. Under some assumptions of the initial data u0(x)u0(x), u1(x)u1(x) and the nonlinear function f(u)f(u), the existence of global weak solutions and global strong solutions are obtained by means of the potential well method.
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Authors
Qun Lin, Yong Hong Wu, Shaoyong Lai,