THE CAUCHY PROBLEM FOR HYPERBOLIC TYPE EQUATIONS AND ITS SOLUTION BY THE METHOD OF CHARACTERISTICS

Abstract

This article explores the Cauchy problem for hyperbolic type equations, focusing on the method of characteristics as a solution technique. The Cauchy problem is a fundamental problem in the theory of partial differential equations, where the goal is to find a solution that satisfies initial conditions given at a specific point in time. For hyperbolic type equations, the method of characteristics is a powerful tool for solving such problems. This method transforms the partial differential equation into a set of ordinary differential equations along certain curves, called characteristics, and provides an efficient way to derive the solution. The article delves into the theoretical foundations of the method, its applications, and discusses the advantages of using this approach for solving hyperbolic type equations. Practical examples and boundary conditions are also examined to illustrate the implementation of the method in various scenarios