Complete families of solutions to the heat equation and generalized heat equation in R^{n}
Abstract
Construction of a complete family of solutions for parabolic equations in three or more space variables is addressed. The simplest case of the heat equation in n space variables and a class of parabolic equations in n space variables with singular coefficients are treated. Recent results in the analytic theory of parabolic equations are invoked in the study. The analysis is presented as a contribution toward development of a more general theory for parabolic equations in three or more variables with variable coefficients.
 Publication:

Journal of Differential Equations
 Pub Date:
 July 1977
 DOI:
 10.1016/00220396(77)901826
 Bibcode:
 1977JDE....25...96C
 Keywords:

 Boundary Value Problems;
 Parabolic Differential Equations;
 Roots Of Equations;
 Thermodynamics;
 Existence Theorems;
 Maximum Principle;
 Polynomials;
 Fluid Mechanics and Heat Transfer