The aims of this paper are to establish theoretical analysis and numerical simulation for a nonlinear wave equation with mixed boundary conditions of Dirichlet and Acoustic type. The theoretical results are about: existence and uniqueness of global solutions, regularity and uniform stability of these global solutions and an exponential decay rate for energy. In the numerical context, simulations are presented using the finite element method in space (with linear and quadratic Lagrange basis), the Crank-Nicolson method in time and, for each discrete time, the Newton’s method is used to solve the nonlinear algebraic system. Furthermore, the energy exponential decay and convergence order (sub-optimal and optimal) are presented numerically.

本文的目的是建立具有狄利克雷和声学混合边界条件的非线性波动方程的理论分析和数值模拟。理论结果是关于：全局解的存在性和唯一性，这些全局解的规律性和均匀稳定性以及能量的指数衰减率。在数值环境中，使用空间中的有限元方法（具有线性和二次拉格朗日基）、时间上的 Crank-Nicolson 方法进行模拟，对于每个离散时间，使用牛顿法求解非线性代数系统。此外，能量指数衰减和收敛顺序（次优和最优）以数值方式呈现。