A Review of Partial Differential Equations of the First Order in Dynamical Systems

Abstract

The first order partial differential equations are studied in this thesis.The relation between the solution of a system of first order partial differential equations and a system of total differential equations and is discussed. The investigation of singular system leads to total differential equations which are integrable under certain integrability conditions. Furthermore; Hamilton-Jacobi partial differential equation (HJPDE) is constructed in both discrete and continuous systems.