Semigroup theory and finite element method applied to a non-linear dissipative wave equation

Abstract

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.