Boundary null controllability of degenerate heat equation as the limit of internal controllability

被引：2
|
作者：
Araujo, B. S. V. [1 ]
Demarque, R. [2 ]
Viana, L. [3 ]
机构：
[1] Univ Fed Campina Grande, Unidade Academ Matemat, Campina Grande, PB, Brazil
[2] Univ Fed Fluminense, Dept Ciencias Nat, Rio das Ostras, RJ, Brazil
[3] Univ Fed Fluminense, Dept Analise, Niteroi, RJ, Brazil
来源：
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2022年 / 66卷
关键词：
Heat equation; Degenerate parabolic equations; Controllability; Observability; Singular perturbations in context of; PDEs; Asymptotic behavior of solutions to; PARABOLIC OPERATORS;
D O I：
10.1016/j.nonrwa.2022.103519
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we recover the boundary null controllability for the degenerate heat equation by analyzing the asymptotic behavior of an eligible family of state-control pairs ((u(epsilon), h(epsilon)))(epsilon > 0) solving corresponding singularly perturbed internal null controllability problems. As in other situations studied in the literature, our approach relies on Carleman estimates and meticulous weak convergence results. However, for the degenerate parabolic case, some specific trace operator inequalities must be obtained, in order to justify correctly the passage to the limit argument. (C)& nbsp;2022 Elsevier Ltd. All rights reserved.
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页数：24
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