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

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.


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