Abstract
In this paper, we are concerned with the general decay result of the quasi-linear wave equation for Kirchhoff type containing Balakrishnan-Taylor damping with a delay in the boundary feedback and acoustic boundary conditions.
Highlights
Let be a bounded domain of Rn, n ≥, with a smooth boundary = ∪
We are concerned with the general decay of solutions of the quasilinear wave equation for Kirchhoff type containing Balakrishnan-Taylor damping with a delay and acoustic boundary condition
System ( . )-( . ) represents a nonlinear viscoelastic equation for Kirchhoff type containing Balakrishnan-Taylor damping with a time-varying delay and acoustic boundary conditions
Summary
We are concerned with the general decay of solutions of the quasilinear wave equation for Kirchhoff type containing Balakrishnan-Taylor damping with a delay and acoustic boundary condition,. ) represents a nonlinear viscoelastic equation for Kirchhoff type containing Balakrishnan-Taylor damping with a time-varying delay and acoustic boundary conditions. In this paper, we study the general decay of solutions for Kirchhoff type containing Balakrishnan-Taylor damping with a time-varying delay and acoustic boundary conditions. This is done by applying the idea presented in [ ] with some necessary modification due to the nature of the problem treated here. If (u , u ) ∈ (H ( ) ∩ V ) × V , y ∈ L ( ), f ∈ L ( × [–τ ( ), ]) and ( . ) is satisfied, the solution (u(t), y(t), z(t)) of ( . )-( . ) is bounded and global in time
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