EXPLICIT SOLUTIONS FOR LINEAR PARTIAL DIFFERENTIAL EQUATIONS

Abstract

We represent analytic functions of real variables by means of functional series with the terms defined in multi-dimensional complex space. That makes possible to obtain a wide class of explicit solutions for linear constant coefficient PDE though in this paper we only consider second order equations . Series solutions often degenerate to finite sums and we pay special attention to this case and construct a basis for the space of polynomial solutions. A number of finite solutions for classic constant coefficient PDEs is given as an example. Particular variable coefficient PDE is considered also. The method is transparent and useful for symbolic calculations. Mathematically it is based upon the classic theory of functions of several complex variables.