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Global Non-negative Approximate Controllability of Parabolic Equations with Singular Potentials

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Trends in Control Theory and Partial Differential Equations

Part of the book series: Springer INdAM Series ((SINDAMS,volume 32))

Abstract

In this work, we consider the linear \(1-d\) heat equation with some singular potential (typically the so-called inverse square potential). We investigate the global approximate controllability via a multiplicative (or bilinear) control. Provided that the singular potential is not super-critical, we prove that any non-zero and non-negative initial state in \(L^2\) can be steered into any neighborhood of any non-negative target in \(L^2\) using some static bilinear control in \(L^\infty \). Besides the corresponding solution remains non-negative at all times.

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Authors and Affiliations

  1. Institut de Mathématiques de Toulouse, UMR CNRS 5219, Université Paul Sabatier Toulouse III, 118 route de Narbonne, 31 062, Toulouse Cedex 4, France

    Judith Vancostenoble

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  1. Judith Vancostenoble
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Correspondence to Judith Vancostenoble .

Editor information

Editors and Affiliations

  1. Laboratoire Jacques-Louis Lions UMR 7598, Sorbonne Université, Paris, France

    Fatiha Alabau-Boussouira

  2. Dipartimento di Matematica “Tullio Levi-Civita”, Università degli Studi di Padova, Padua, Italy

    Fabio Ancona

  3. Dipartimento di Matematica, Università di Roma “Tor Vergata”, Rome, Italy

    Alessio Porretta

  4. Dipartimento di Ingegneria Civile e Ingegneria Informatica, Università di Roma “Tor Vergata”, Rome, Italy

    Carlo Sinestrari

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Vancostenoble, J. (2019). Global Non-negative Approximate Controllability of Parabolic Equations with Singular Potentials. In: Alabau-Boussouira, F., Ancona, F., Porretta, A., Sinestrari, C. (eds) Trends in Control Theory and Partial Differential Equations. Springer INdAM Series, vol 32. Springer, Cham. https://doi.org/10.1007/978-3-030-17949-6_13

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