Convolution product methods for solving partial differential equations

Abstract

In this thesis, the double convolutions properties are studied. We solved first order non-homogenous Partial Differential Equations (PDE) having non-homogenous initial condition by using reduction to first-order PDE technique. The Green's formula, Green's function and generalized function and the reduction to first-order PDE techniques have been used to solve the non-homogenous wave equation with initial condition. The non-homogenous terms used in this study are convolution terms. Furthermore the uniqueness and continuity of non-homogenous wave equation discussed.