English

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.

Keywords

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

R2 v1 2026-06-22T10:00:36.338Z