Abstract
Motivated by the recent known results as regards the existence and exponential decay of solutions for wave equations, this paper is devoted to the study of an N-dimensional nonlinear wave equation with a nonlocal boundary condition. We first state two local existence theorems. Next, we give a sufficient condition to guarantee the global existence and exponential decay of weak solutions. The main tools are the Faedo-Galerkin method and the Lyapunov method.
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