Control Problem Related to a 2D Parabolic–Elliptic Chemo-Repulsion System with Nonlinear Production-Reference-Cited by-同舟云学术

Control Problem Related to a 2D Parabolic–Elliptic Chemo-Repulsion System with Nonlinear Production

Published:2023-10-21 Issue:10 Volume:15 Page:1949
ISSN:2073-8994
Container-title:Symmetry
language:en
Short-container-title:Symmetry

Author:

Mallea-Zepeda Exequiel¹^ORCID,Medina Luis²^ORCID

Affiliation:

1. Departamento de Matemáticas, Universidad Católica del Norte, Av. Angamos 0610, Antofagasta 1240000, Chile

2. Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Av. Angamos 601, Antofagasta 1240000, Chile

Abstract

In this work, we analyze a bilinear optimal control problem related to a 2D parabolic–elliptic chemo-repulsion system with a nonlinear chemical signal production term. We prove the existence of global optimal solutions with bilinear control, and applying a generic result on the existence of Lagrange multipliers in Banach spaces, we obtain first-order necessary optimality conditions and derive an optimality system for a local optimal solution.

Publisher

MDPI AG

Subject

Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2073-8994/15/10/1949/pdf

Reference31 articles.

1. On some models describing cellular movement: The macroscopic scale;Bol. Soc. Esp. Mat. Apl.,2009

2. Aggregation, blowup and collapse: The ABC’S of taxis in reinforced random walks;Othmer;SIAM J. Appl. Math.,1997

3. Initiation of slime mold aggregation viewed as an instability;Keller;J. Theor. Biol.,1970

4. Model for chemotaxis;Keller;J. Theor. Biol.,1971

5. Chemotaxis-fluid coupled model for swimming bacteria with nonlinear diffusion: Global existence and asymptotic behavior;Lorz;Discret. Contin. Dyn. Syst.,2010