Classical solutions for a class of IVP for nonlinear two-dimensional wave equations via new fixed point approach

Abstract

This paper devoted to research a classical solutions for a range of two-dimensional problems associated with the propagation of nonlinear waves subjected with a class of initial value problems of nonlinear equations in hyperbolic type. A new fixed point approach is used to prove the existence of classical positive solutions of the considered IVP. The results in the manuscript are provided with examples.