Abstract
In this paper, we investigate the well-posedness as well as optimal decay rate estimates of the energy associated with a Kirchhoff-Carrier problem in n-dimensional bounded domain under an internal finite memory. The considered class of memory kernels is very wide and allows us to derive new and optimal decay rate estimates then those ones considered previously in the literature for Kirchhoff-type models.
Highlights
When equation (1.1) is supplemented by some type of dissipative mechanism, which allows us, roughly speaking, to derive decay rate estimates for the solutions of the linearized problen of (1.1), it is possible to recover the global solvability in time
We investigate the well-posedness as well as optimal decay rate estimates of the energy associated with the following Kirchhoff-Carrier problem with memory:
Where Ω is a bounded domain in Rn, n ∈ N∗, with smooth boundary ∂Ω := Γ
Summary
We are led naturally to consider the Kirchhoff equation subject to a dissipative term which guarantees the decay properties of the linearized problem. We investigate the well-posedness as well as optimal decay rate estimates of the energy associated with the following Kirchhoff-Carrier problem with memory: The assumption given in (1.7), firstly introduced in [20], is much more general and allows us to consider a wide class of kernels, and get new and optimal decay rate estimates those ones considered previously in the literature for the linear viscoelastic wave equation.
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