Resolution of Partial Differential Equations of the Hyperbolic Type with Source Term By the Formula of D'Alembert

Abstract

In the present work, we study a non-homogeneous second order partial hyperbolic differential equation, its canonical form, its resolution using D’Alembert’s formula and  Green’s theorem. Only mixed initial conditions that are not homogeneous are required to solve this problem. There are several physical problems that lead to this type of mathematical model, so this technique of resolution contributes to the knowledge of finding explicit solutions of problems such as two-dimensional wave type. Within the results the explicit solution of three cases is generated: regarding the homogeneity and non-homogeneity of the initial conditions and the term source, from the point of view of analytical solution for continuous functions.