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

Autor:	Galo-Mendoza, L., López-García, M.
Rok vydání:	2023
Předmět:	Mathematics - Analysis of PDEs Mathematics - Optimization and Control 35K65 34B24 30E05 93B05 93B60
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
Externí odkaz:	http://arxiv.org/abs/2308.07290 Zobrazit plný text záznamu View this record from Arxiv