Boundary controllability for a 1D degenerate parabolic equation with a Robin boundary condition
Autor: | Galo-Mendoza, L., López-García, M. |
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Rok vydání: | 2023 |
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Druh dokumentu: | Working Paper |
Popis: | 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. Comment: arXiv admin note: substantial text overlap with arXiv:2304.00178, arXiv:2302.01197 |
Databáze: | arXiv |
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