Approximate controllability of a semilinear elliptic problem in periodically perforated domains

In this paper, we study the controllability of a semilinear second order elliptic boundary value problem in a periodically perforated domain, where the control is distributed in an open subset of the domain. Compared to existing literature, the holes in this control problem can intersect the control...

Full description

Saved in:
Bibliographic Details
Published in:Journal of mathematical analysis and applications 2024-02, Vol.530 (1), p.127676, Article 127676
Main Authors: Conca, Carlos, Jose, Editha C., Mishra, Indira
Format: Article
Language:English
Subjects:
Approximate control
Homogenization
Perforated domain
Semilinear elliptic problem
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, we study the controllability of a semilinear second order elliptic boundary value problem in a periodically perforated domain, where the control is distributed in an open subset of the domain. Compared to existing literature, the holes in this control problem can intersect the control zone. We study L2 and H1-approximate controllability for the problem and we prove the homogenization results for the control problem in an ε-periodically perforated domain. The holes are of same size as ε with the coefficients of state equation, and the cost functional being rapidly oscillating.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2023.127676