One-dimensional heat equation with discontinuous conductance
Probability
2013-12-31 v1
Abstract
We study a second-order parabolic equation with divergence form elliptic operator, having piecewise constant diffusion coefficients with two points of discontinuity. Such partial differential equations appear in the modelization of diffusion phenomena in medium consisting of three kind of materials. Using probabilistic methods, we present an explicit expression of the fundamental solution under certain conditions. We also derive small-time asymptotic expansion of the PDE's solutions in the general case. The obtained results are directly usable in applications.
Cite
@article{arxiv.1312.7396,
title = {One-dimensional heat equation with discontinuous conductance},
author = {Zhen-Qing Chen and Mounir Zili},
journal= {arXiv preprint arXiv:1312.7396},
year = {2013}
}