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arXiv · 2308.07290

Boundary controllability for a 1D degenerate parabolic equation with a Robin boundary condition

L. Galo-Mendoza·M. López-García
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Abstract

In this paper we prove the null controllability of a one-dimensional degenerate parabolic equation with a weighted Robin boundary condition at the left endpoint, where the potential has a singularity. We use some results from the singular Sturm-Liouville theory to show the well-posedness of our system. We obtain a spectral decomposition of a degenerate parabolic operator with Robin conditions at the endpoints, we use Fourier-Dini expansions and the moment method introduced by Fattorini and Russell to prove the null controllability and to obtain an upper estimate of the cost of controllability. We also get a lower estimate of the cost of controllability by using a representation theorem for analytic functions of exponential type.

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L. Galo-Mendoza, M. López-García. 2023-08-14. Boundary controllability for a 1D degenerate parabolic equation with a Robin boundary condition. https://arxiv.org/abs/2308.07290

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