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Main Authors:	Barreira, João Carlos, Sonego, Maicon, Zuazua, Enrique
Format:	Preprint
Published:	2025
Subjects:	Analysis of PDEs
Online Access:	https://arxiv.org/abs/2511.01453
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author	Barreira, João Carlos Sonego, Maicon Zuazua, Enrique
author_facet	Barreira, João Carlos Sonego, Maicon Zuazua, Enrique
contents	We investigate the controllability of a generalized diffusive Lotka-Volterra competition model for two species, incorporating boundary controls and an interior multiplicative control. Considering a smooth, bounded N-dimensional domain, we analyze ecologically pertinent scenarios characterized by constraints on both the controls and system states. Our results demonstrate how integrated control strategies can effectively overcome the limitations identified in previous studies. We prove two main results: (1) asymptotic controllability to single-species survival steady states under arbitrary system parameters, ensured by a combination of boundary and interior controls which act jointly to stabilize the system; and (2) finite-time controllability to a specific heterogeneous coexistence steady state via a two-phase strategy - first steering the system near the target with boundary control, then activating an interior multiplicative control in a localized region. The strong synergy between the two control mechanisms is crucial in both cases. We also analyze extinction dynamics and homogeneous coexistence, and support our findings with numerical simulations. The work concludes with perspectives for future research.
format	Preprint
id	arxiv_https___arxiv_org_abs_2511_01453
institution	arXiv
publishDate	2025
record_format	arxiv
spellingShingle	Boundary and Interior Control in a Diffusive Lotka-Volterra Model Barreira, João Carlos Sonego, Maicon Zuazua, Enrique Analysis of PDEs We investigate the controllability of a generalized diffusive Lotka-Volterra competition model for two species, incorporating boundary controls and an interior multiplicative control. Considering a smooth, bounded N-dimensional domain, we analyze ecologically pertinent scenarios characterized by constraints on both the controls and system states. Our results demonstrate how integrated control strategies can effectively overcome the limitations identified in previous studies. We prove two main results: (1) asymptotic controllability to single-species survival steady states under arbitrary system parameters, ensured by a combination of boundary and interior controls which act jointly to stabilize the system; and (2) finite-time controllability to a specific heterogeneous coexistence steady state via a two-phase strategy - first steering the system near the target with boundary control, then activating an interior multiplicative control in a localized region. The strong synergy between the two control mechanisms is crucial in both cases. We also analyze extinction dynamics and homogeneous coexistence, and support our findings with numerical simulations. The work concludes with perspectives for future research.
title	Boundary and Interior Control in a Diffusive Lotka-Volterra Model
topic	Analysis of PDEs
url	https://arxiv.org/abs/2511.01453

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