In this paper, we consider the Dirichlet problem for a nonlinear wave equation with Balakrishnan–Taylor term. We establish the local existence is established by the linearization method together with the Faedo–Galerkin method. Next, we prove an exponential energy decay result by suitable Lyapunov functionals.

中文翻译：

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具有 Balakrishnan-Taylor 项的非线性波动方程狄利克雷问题的存在性和指数衰减*

在本文中，我们考虑具有 Balakrishnan-Taylor 项的非线性波动方程的 Dirichlet 问题。我们通过线性化方法和 Faedo-Galerkin 方法建立局部存在。接下来，我们通过合适的李雅普诺夫泛函证明了指数能量衰减结果。