Existence of Solutions of Boundary Value Problem for Nonlinear One-Dimensional Wave Equations by Fixed Point Method

Abstract

In this article, we investigate the solutions for a class of initial boundary value problems for nonlinear one-dimensional wave equations using a fixed point method. The findings consider initial and boundary data which lead to determining the nature of classes of the nonlinear one-dimensional wave equation. The obtained results indicate the availability of nonnegative solutions which are proved using the method of the fixed point. A new fixed point approach is effective and used as a definitive modeling method to prove the existence of nonnegative solutions for a class of initial boundary value problems based on recent theoretical arguments. The results in this study are considered with examples.