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The cost of approximate controllability of heat equation with dynamical boundary conditions

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I. Boutaayamou, S. E. Chorfi, L. Maniar, O. Oukdach

Analysis of PDEs · Submitted 11 Jun 2020

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Combining new developed Carleman estimates and some optimization techniques, we obtain explicit bounds of the minimal norm control.

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arXiv ID2006.06711 (version 1)
Pith IDH5PM6SE6, Pith's permanent record of this paper and its review
CitationI. Boutaayamou, L. Maniar, O. Oukdach, S. E. Chorfi. "The cost of approximate controllability of heat equation with dynamical boundary conditions." arXiv:2006.06711 (2020). https://pith.science/paper/H5PM6SE6
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,443 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.09 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.60 · compares with prior results 0.05 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We consider the heat equation with dynamic bounary conditions involving gradient terms in a bounded domain. In this paper we study the cost of approximate controllability for this equation. Combining new developed Carleman estimates and some optimization techniques, we obtain explicit bounds of the minimal norm control. We consider the linear and the semilinear cases.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We consider the heat equation with dynamic bounary conditions involving gradient terms in a bounded domain. background 0.97 0.23 0.02 asserted 0.89
s1 In this paper we study the cost of approximate controllability for this equation. contribution 0.93 0.78 0.06 asserted 0.82
s2 Combining new developed Carleman estimates and some optimization techniques, we obtain explicit bounds of the minimal norm control. result 0.36 0.96 0.77 asserted 1.00
s3 We consider the linear and the semilinear cases. contribution 0.76 0.49 0.04 asserted 0.88

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We consider the heat equation with dynamic bounary conditions involving gradient terms in a bounded domain. In this paper we study the cost of approximate controllability for this equation. Combining new developed Carleman estimates and some optimization techniques, we obtain explicit bounds of the minimal norm control. We consider the linear and the semilinear cases.

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