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In this paper we study the initial-boundary value problem of the multidimensional viscoelasticity equation with nonlinear source term u tt -Δut - ΣNi =1 δ δxi si(u xi) = f (u). By using the potential well method, we first prove the global existence. Then we prove that when time t→+∞, the solution decays to zero exponentially under some assumptions on nonlinear functions and the initial data. © 2013 Xu et al.; licensee Springer.

Asymptotic behaviour of solution for multidimensional viscoelasticity equation with nonlinear source term