Generalization of Separation of Variables n-Harmonic Equation m Dimension and Unbounded Boundary Value Problem

Abstract

The method of separation of variables is significant, it has been applied to physics, engineering , chemistry and other fields. It allows to reduce the diffculity of problems by separating the variables from partial differential equation system into ordinary differential equations system. However, this method has complexity in higher order partial differential equations. In this reserach, we generalize this method by using multinomial theorem of n-harmonic equation to solve n-harmonic equation with $m$ dimension and then solving an important class of partial differential equations with unbounded boundary conditions. Additionaly, application of convolution.