Exponential decay of solutions to a viscoelastic equation with nonlinear localized damping with source term

L. E. Torres Guardia, V. C. Barrantes e F. L. Barboza
In this paper we consider the nonlinear viscoelastic equation
u_{tt} − \Delta u + \int_0^t g(t − \tau)\Delta u(\tau) d\tau + a(x)|u_t |^{m−1} u_t − |u|^{p−1} u = 0,
in a bounded domain. By introducing a potential well we establish the global existence . Furthermore we prove an exponential decay result for $m > 1$.
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