THE STUDY OF CAUCHY PROBLEM FOR ONEDIMENSIONALWAVE EQUATIONS

Abstract

The Wave equation is second order linear partial differential equations that concerns different physical phenomena. The Cauchy problem for wave equation is to find the solution of the wave equation subject to initial conditions. Thus in this thesis we studies the existence, uniqueness and stability the Cauchy problem for wave equations. We find that the solution of the Cauchy problem for one dimensional wave equation exist and continuously depends on initial conditions. We examine the solution using analytical method and computational method. Special we find the solution by separation of the variable method, d’Alembert formula, Mathematica software and computer C++ programming.