Modeling of a heat equation with a Dirac density
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.
math.AP↗