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New general decay result for a class of neutral viscoelastic equations. (English) Zbl 1475.35047

Summary: We are concerned with the decay estimate of a neutral viscoelastic equation with nonlinear boundary damping and boundary memory effect. We obtain a general decay theorem for the neutral viscoelastic equation by showing that its system energy is controlled by a solution of the associated ODE. Moreover, distinguished from the previous compactness-uniqueness method, we propose an analytical approach to estimate the low-order terms by using the Sobolev imbedding theory.

MSC:

35B40 Asymptotic behavior of solutions to PDEs
35L20 Initial-boundary value problems for second-order hyperbolic equations
35R09 Integro-partial differential equations
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