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arXiv · 1506.07936

Modeling of a heat equation with a Dirac density

Scott W. Hansen·Jose de Jesus Martinez
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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.

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Scott W. Hansen, Jose de Jesus Martinez. 2015-09-23. Modeling of a heat equation with a Dirac density. https://arxiv.org/abs/1506.07936

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