A bilinear form of the variational principle with vanishing parameter

Abstract

A variational principle whose Lagrangian function generates a hyperbolic heat conduction equation is exhibited. The main characteristic of this principle is that it contains two temperature fields that enter bilinearly into the Lagrangian function. These two fields are interpreted as two mutually independent approximate temperature profiles which are potentially competent to describe rationally the real physical temperature distribution. The proposed variational principle is used as a starting point for finding approximate solutions of the classical, i.e. Fourier's, heat conduction theory, by employing the vanishing parameter technique and the direct methods of variational calculus.