Stability for a coupled system of wave equations of Kirchhoff type with nonlocal boundary conditions. (English) Zbl 1036.35141

Ferreira, Jorge; Pereira, Ducival C.; Santos, Mauro L.

Electron. J. Differ. Equ. 2003, Paper No. 85, 17 p. (2003).

The authors prove the existence and uniqueness of solutions to a system of second-order nonlinear partial differential equations of Kirchhoff type, with boundary conditions that contain integral terms. The asymptotic behavior of solutions is also studied in terms of a related energy functional. The existence proof is carried out with the help of a Galerkin type method. The study of asymptotic properties relies on the construction of a Lyapunov functional and the use of integral and differential inequalities.

Reviewer: Sergiu Aizicovici (Athens/Ohio)

MSC:

35L70	Second-order nonlinear hyperbolic equations
35L55	Higher-order hyperbolic systems
35B05	Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs

Keywords:

Galerkin method; asymptotic behavior; Lyapunov functionals