Search

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. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we consider the initial-boundary value problem for a nonlinear Kirchhoff type equation with the damping term and spring boundary conditions. We establish the global existence and uniqueness of solutions to this problem in time, and give an example and simulation to illustrate our results. For the proof, we use the Faedo–Galerkin approximate method. Finally, we study the asymptotic behavior of solutions and some of its simulation results. Results of this paper are able to apply industrial parts such as a typical model widely used to represent threads, wires, magnetic tapes, belts, band saws, and so on. [Copyright &y& Elsevier]

In this paper, we consider a quasilinear viscoelastic wave equation with acoustic boundary conditions. Under some appropriate assumption on the relaxation function g, the function Φ, p>max{ρ+2,m,q,2}, and the initial data, we prove a global nonexistence of solutions for a quasilinear viscoelastic wave equation with positive initial energy. [ABSTRACT FROM AUTHOR]