Tools Used from Mathematics in The Study of a Riemannian Wave Equation to Prevent the Collapse of Bridges

Abstract

In this research, the study of dynamical systems is addressed in the area of partial differential equations, focusing on a mathematical model represented by a Dirichlet-type wave equation on a Riemannian manifold. The goal is to understand the importance of mathematics in optimizing dampers and locating them in curved structures, such as bridges, to prevent their collapse.