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Erschienen in:
Some Remarks on the Dirichlet Problem for the Degenerate Eikonal Equation Kapitel lesen Erstes Kapitel lesen

2019 | OriginalPaper | Buchkapitel

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

verfasst von : Judith Vancostenoble

Erschienen in: Trends in Control Theory and Partial Differential Equations

Verlag: Springer International Publishing

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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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Vorheriges Kapitel Asymptotic Analysis of a Cucker–Smale System with Leadership and Distributed Delay
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Metadaten
Titel
Global Non-negative Approximate Controllability of Parabolic Equations with Singular Potentials
verfasst von
Judith Vancostenoble
Copyright-Jahr
2019
Buch
Trends in Control Theory and Partial Differential Equations

Print ISBN: 978-3-030-17948-9

Electronic ISBN: 978-3-030-17949-6

Copyright-Jahr: 2019

DOI
https://doi.org/10.1007/978-3-030-17949-6_13