Modeling of a heat equation with a Dirac density

Abstract

We consider a linear hybrid system composed by two rods connected by a thin wall of length 2ε and density 1/2ε. 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.

10 pages, typos corrected, fixed references, matches version to be submitted to Proceedings of Dynamic Systems and Applications