Issue |
ESAIM: COCV
Volume 30, 2024
|
|
---|---|---|
Article Number | 28 | |
Number of page(s) | 35 | |
DOI | https://doi.org/10.1051/cocv/2024018 | |
Published online | 09 April 2024 |
Controlled traveling profiles for models of invasive biological species
Department of Mathematics, Penn State University, University Park, PA 16802, USA
* Corresponding author: axb62@psu.edu
Received:
20
February
2023
Accepted:
8
March
2024
We consider a family of controlled reaction-diffusion equations, describing the spatial spreading of an invasive biological species. For a given propagation speed c ∈ IR, we seek a control with minimum cost, which achieves a traveling profile with speed c. Since our goal is to slow down or even reverse the contamination, we always assume c > c*, where c* is the speed of an uncontrolled traveling profile. For various nonlinear models, the existence of an optimal control is proved, together with necessary conditions for optimality. In the last section, we study a case where the wave speed cannot be modified by any control with finite cost. The present analysis is motivated by the recent results in A. Bressan, et al. Math. Models Methods Appl. Sci. 32 (2022) 1109–1140. and A. Bressan, et al. J. Differ. Equ. 361 (2023) 97–137, showing how a control problem for a reaction-diffusion equation can be approximated by a simpler problem of optimal control of a moving set.
Mathematics Subject Classification: 49N90 / 35C07 / 49J05 / 49K05
Key words: Controlled traveling profile / optimal control / reaction-diffusion equation / invasive biological population
© The authors. Published by EDP Sciences, SMAI 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.