Energy decay for nonlinear Kirchhoff-like type wave equation with nonlinear velocity feedback

摘要

We investigate on the global existence and energy decay of solutions to the following Kirchhoff-like type wave equation equations where′, = d over dt, Ω is a bounded domain in Rⁿ with smooth boundary Γ. The matrix A(u) has the form equations where aij(s) are smooth functions on R and ∥ · ∥ denote the norm of Sobolev space L2(Ω).