Solution of Periodic Hyperbolic Differential Problem with Initial Control Function

Abstract

This work investigates the problem of a periodic hyperbolic equation formulated in a bounded domain with a convection term and weakly sourced nonlinear functions. The purpose of this work is to analyze the existence of solutions to the control initial problem using ideas of hyperbolic and periodicity of first derivatives and control starting conditions, as well as some properties of some inequalities offered to investigate this topic.