This paper is devoted to the study of a nonlinear Kirchhoff-Carrier wave
equation in an annular associated with nonhomogeneous Dirichlet conditions.
At first, by applying the Faedo-Galerkin, we prove existence and uniqueness
of the solution of the problem considered. Next, by constructing Lyapunov
functional, we prove a blow-up result for solutions with a negative initial
energy and establish a sufficient condition to obtain the exponential decay of
weak solutions.
Blow-up solutions, global existence, and exponential decay estimates for second order parabolic problems