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**Energy decay rates for solutions of the Kirchhoff type wave equation with boundary damping and source terms.**
*(English)*
Zbl 1415.35177

Summary: In this work, we are concerned with uniform stabilization for an initial-boundary value problem associated with the Kirchhoff type wave equation with feedback terms and memory condition at the boundary. We prove that the energy decays exponentially when the boundary damping term has a linear growth near zero and polynomially when the boundary damping term has a polynomial growth near zero. Furthermore, we study the decay rate of the energy without imposing any restrictive growth assumption on the damping term near zero.

### MSC:

35L20 | Initial-boundary value problems for second-order hyperbolic equations |

35B35 | Stability in context of PDEs |

35B40 | Asymptotic behavior of solutions to PDEs |

35R09 | Integro-partial differential equations |

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\textit{T. G. Ha}, J. Integral Equations Appl. 30, No. 3, 377--415 (2018; Zbl 1415.35177)

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