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Existence and uniform decay for a non‐linear viscoelastic equation with strong damping

Marcelo M. CavalcantiDepartamento de Matemática, Universidade Estadual de Maringá, 87020-900 Maringá, PR, BrazilV. N. Domingos CavalcantiDepartamento de Matemática, Universidade Estadual de Maringá, 87020-900 Maringá, PR, BrazilJorge FerreiraDepartamento de Matemática, Universidade Estadual de Maringá, 87020-900 Maringá, PR, Brazil

2001en

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Abstract This paper is concerned with the non‐linear viscoelastic equation We prove global existence of weak solutions. Furthermore, uniform decay rates of the energy are obtained assuming a strong damping Δ u t acting in the domain and provided the relaxation function decays exponentially. Copyright © 2001 John Wiley & Sons, Ltd.

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DOI: 10.1002/mma.250

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