We study the wave equation with a non-linear dissipative term associated to a bidimensional membrane with fixed boundary. We use the semigroup theory to consider the existence and uniqueness of solutions to the problem and we implement the finite element method to analyse the vibrating evolutionary equation. In particular we use Comsol Multiphysics software with a rectangular mesh to analyze the corresponding evolutionary system. We mention that this system can appear, for example, in the diaphragm of a centrifugal pump in mining processes.

中文翻译：

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半群理论和有限元法在非线性耗散波方程中的应用

我们研究具有与固定边界的二维膜相关的非线性耗散项的波动方程。我们利用半群理论考虑问题解的存在性和唯一性，并采用有限元方法对振动演化方程进行分析。特别是，我们使用具有矩形网格的 Comsol Multiphysics 软件来分析相应的演化系统。我们提到，该系统可以出现在采矿过程中的离心泵的隔膜中。