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On the cost of reaching an attainable state for the boundary-controlled 1-D heat equation
Abstract
We consider the heat equation in an interval of the real line, with null initial condition, and Dirichlet boundary controls. We study the cost of reaching an attainable state at some time T>0. Precisely, given a state in the interval that we know is reachable by suitable boundary controls, we estimate the size of the smallest controls that reach it, in terms of an appropriate norm of this state. Our estimate is optimal in some sense as the time horizon goes to $0$.
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BibTeX
@misc{glass2026cost,
title = {{On the cost of reaching an attainable state for the boundary-controlled 1-D heat equation}},
author = {Olivier Glass},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.08842},
eprint = {2609.08842},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08842},
}
RIS
TY - UNPB
TI - On the cost of reaching an attainable state for the boundary-controlled 1-D heat equation
AU - Olivier Glass
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2609.08842
UR - https://arxiv.org/abs/2609.08842
AB - We consider the heat equation in an interval of the real line, with null initial condition, and Dirichlet boundary controls. We study the cost of reaching an attainable state at some time T>0. Precisely, given a state in the interval that we know is reachable by suitable boundary controls, we estimate the size of the smallest controls that reach it, in terms of an appropriate norm of this state. Our estimate is optimal in some sense as the time horizon goes to $0$.
ER -