Work

Controllability issues for parabolic–elliptic systems involving nonlocal couplings

Year: 2025

Type: article

Abstract: This work addresses controllability properties for some systems of partial differential equations in which the main feature is the coupling through nonlocal integral terms. In the first part, we study a nonlinear parabolic–elliptic system arising in mathematical biology and, using recently developed techniques, we show how Carleman estimates can be directly used to handle the nonlocal terms, allowing us to implement well-known strategies for controlling coupled systems and nonlinear problems. In the second part, we investigate fine controllability properties of a simplified 1-d linear nonlocal coupled system using spectral analysis techniques. In those cases, we will see that the controllability of the concerned model can fail and it will depend on particular choices and combinations of local and nonlocal couplings.

Source: Journal of Evolution Equations

DOI: 10.1007/s00028-025-01133-2

Authors: Kuntal Bhandari, Víctor Hernández-Santamaría

Institutions: Czech Academy of Sciences, Czech Academy of Sciences, Institute of Mathematics, Universidad Nacional Autónoma de México

Language: English

Topic: Stability and Controllability of Differential Equations

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

Funders: Akademie Věd České Republiky, Dirección General de Asuntos del Personal Académico, Universidad Nacional Autónoma de México