Third Boundary-Value Problem of the Heat Conduction Equation for a System with Plane-Parallel Boundaries
Mathematical Physics
2007-05-23 v1 math.MP
Abstract
We obtained a new representation of a solution of the heat conduction equation with boundary condition of the third kind for a layer. The result is presented as a superposition of fundamental solutions for an unbounded system with variable coefficients, the explicit form of which is given. We consider the well-known problem of the evolution of the temperature field initially uniformly distributed in a layer. The distribution of the temperature field is represented in terms of the obtained functions.
Cite
@article{arxiv.math-ph/0102021,
title = {Third Boundary-Value Problem of the Heat Conduction Equation for a System with Plane-Parallel Boundaries},
author = {A. S. Usenko},
journal= {arXiv preprint arXiv:math-ph/0102021},
year = {2007}
}
Comments
16 pages, 2 figures, RevTeX