Modeling of a heat equation with a Dirac density
Analysis of PDEs
2015-09-24 v2
Abstract
We consider a linear hybrid system composed by two rods connected by a thin wall of length 2{\epsilon} and density 1/2{\epsilon}. By passing to a limit, we obtain a system describing heat flow of two rods connected by a singular point whose dynamics are governed by a partial differential equation. We prove that solutions of the approximate system converge weakly to solutions of the limiting system.
Cite
@article{arxiv.1506.07936,
title = {Modeling of a heat equation with a Dirac density},
author = {Scott W. Hansen and Jose de Jesus Martinez},
journal= {arXiv preprint arXiv:1506.07936},
year = {2015}
}
Comments
10 pages, typos corrected, fixed references, matches version to be submitted to Proceedings of Dynamic Systems and Applications