Local null controllability of a parabolic-elliptic chemotaxis system by a Neumann boundary control
Abstract
We prove local null controllability for a parabolic equation coupled to an elliptic equation on a bounded interval. The drift depends on the elliptic variable, and a single control acts through the Neumann condition at the left endpoint. For every positive control time and every locally Lipschitz drift function, sufficiently small initial data in L∞ can be driven to zero by an L∞ boundary control. To construct the control, we extend the linear equation to a larger interval using an even extension of the initial datum and an odd extension of the drift. A distributed L2 control in the added interval then gives a boundary control on the original interval. A heat kernel estimate bounds the derivative trace needed for this construction. We obtain the nonlinear result by a set-valued fixed point argument.
Related
- Carleman estimates for a nonconservative Timoshenko beam involving Dirichlet-Neumann boundary conditions and application to exact controllability
- Propagation dynamics of a parabolic-elliptic chemotaxis model in a time-periodic shifting environment
- Null-controllability for some linear parabolic systems with controls acting on different parts of the domain and its boundary
- Boundary approximate controllability of some linear parabolic systems
- A doubly nonlinear parabolic problem with variable exponents, homogeneous Neumann boundary conditions and generalized logistic source
BibTeX
@misc{bapu2026local,
title = {{Local null controllability of a parabolic-elliptic chemotaxis system by a Neumann boundary control}},
author = {Mohmedmunavvar Mubarak Bapu},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.02621},
eprint = {2611.02621},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.02621},
}
RIS
TY - UNPB
TI - Local null controllability of a parabolic-elliptic chemotaxis system by a Neumann boundary control
AU - Mohmedmunavvar Mubarak Bapu
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.02621
UR - https://arxiv.org/abs/2611.02621
AB - We prove local null controllability for a parabolic equation coupled to an elliptic equation on a bounded interval. The drift depends on the elliptic variable, and a single control acts through the Neumann condition at the left endpoint. For every positive control time and every locally Lipschitz drift function, sufficiently small initial data in L^∞ can be driven to zero by an L^∞ boundary control. To construct the control, we extend the linear equation to a larger interval using an even extension of the initial datum and an odd extension of the drift. A distributed L^2 control in the added interval then gives a boundary control on the original interval. A heat kernel estimate bounds the derivative trace needed for this construction. We obtain the nonlinear result by a set-valued fixed point argument.
ER -