Abstract
In this paper, we consider the initial boundary value problem for a viscoelastic wave equation with nonlinear boundary source term. First of all, we introduce a family of potential wells and prove the invariance of some sets. Then we establish the existence and nonexistence of global weak solution with small initial energy under suitable assumptions on the relaxation function , nonlinear function , the initial data and the parameters in the equation. Furthermore, we obtain the global existence of weak solution for the problem with critical initial conditions and .
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