Modeling and controllability of a heat equation with a point mass

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2015-01-01
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Martínez, José de Jesús
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Scott Hansen
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Mathematics
Abstract

In this thesis, we propose a linear hybrid system describing heat flow on a medium composed by two rods connected by a point mass. We show that such a system can be obtained from a system describing heat flow of two rods connected by a thin wall of width 2є and density of 1/2є. By passing to a weak limit, we obtain the desired system.

We then show that the limiting system is null controllable with Dirichlet boundary control when the system's parameters satisfy a certain condition. Lastly, we consider simple parameters to show that the point mass system is null controllable with either Dirichlet or Neumann boundary control at one end.

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Thu Jan 01 00:00:00 UTC 2015