Boundary controllability for a 1D degenerate parabolic equation with drift and a singular potential

Leandro Galo-Mendoza; Marcos López-García

doi:10.3934/mcrf.2023027

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2024, Volume 14, Issue 3: 848-866. Doi: 10.3934/mcrf.2023027

This issue Previous Article Approximate controllability for some retarded integrodifferential inclusions using a version of the Leray-Schauder fixed point theorem for the multivalued maps Next Article A long-term optimal consumption and investment problem with partial information

Boundary controllability for a 1D degenerate parabolic equation with drift and a singular potential

Leandro Galo-Mendoza and
Marcos López-García^,

Instituto de Matemáticas-Unidad Cuernavaca, Universidad Nacional Autónoma de México, Av. Universidad S/N, Cuernavaca, Morelos, C.P. 62210, México

^*Corresponding author: Marcos López-García
^*Corresponding author: Marcos López-García

Received: July 2022

Revised: March 2023

Early access: August 2023

Published: September 2024

The second author was partially supported by DGAPA-UNAM [PAPIIT IN109522], and CONACYT-México [A1-S-17475]. The first author was supported by a grant from CONACyT-México

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Abstract

We prove the null controllability of a one-dimensional degenerate parabolic equation with drift and a singular potential. We study the case when the potential arises at the left endpoint and a weighted Dirichlet boundary control is located at this point. We get a spectral decomposition of a suitable operator, defined in a weighted Sobolev space, involving Bessel functions and their zeros, then we use the moment method by Fattorini and Russell to obtain an upper estimate of the cost of controllability. We also obtain a lower estimate of the cost of controllability by using a representation theorem for analytic functions of exponential type.

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Mathematics Subject Classification: Primary: 35K65, 93B05; Secondary: 30E05, 93B60.

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