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The Case for Differential Geometry in the Control of Single and Coupled PDEs: The Structural Acoustic Chamber

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Geometric Methods in Inverse Problems and PDE Control

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 137))

Abstract

In line with the title of the IMA Summer Program—Geometric Methods in Inverse Problems and PDE Control—the aim of the present article may be summarized as follows: we intend to provide a relatively updated survey (subject to space limitations) of results on exact boundary controllability and uniform boundary stabilization of certain general classes of single Partial Differential Equations as well as of classes of systems of coupled PDEs (in dimension strictly greater than one), that have become available in recent years through novel approaches based on differential (Riemannian) geometric methods.

Research partially supported by the National Science Foundation under Grant DMS-0104305 and by the Army Research Office under Grant DAAD19-02-1-0179.

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Authors and Affiliations

  1. School of Mathematics, Vincent Hall, University of Minnesota, 55455, Minneapolis, MN, USA

    R. Gulliver & W. Littman

  2. Department of Mathematics, Kerchof Hall, University of Virginia, 22904, Charlottesville, VA, USA

    I. Lasiecka & R. Triggiani

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  1. R. Gulliver
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  2. W. Littman
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  3. I. Lasiecka
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  4. R. Triggiani
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Editors and Affiliations

  1. Department of Mathematics, University of Pennsylvania, 19104-6395, Philadelphia, PA, USA

    Christopher B. Croke

  2. Department of Mathematics, Rutgers University, 08903, New Brunswick, NJ, USA

    Michael S. Vogelius

  3. Department of Mathematics, University of Washington, 98195-4350, Seattle, WA, USA

    Gunther Uhlmann

  4. Department of Mathematics, University of Virginia, 22903, Charlottesville, VA, USA

    Irena Lasiecka

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Gulliver, R., Littman, W., Lasiecka, I., Triggiani, R. (2004). The Case for Differential Geometry in the Control of Single and Coupled PDEs: The Structural Acoustic Chamber. In: Croke, C.B., Vogelius, M.S., Uhlmann, G., Lasiecka, I. (eds) Geometric Methods in Inverse Problems and PDE Control. The IMA Volumes in Mathematics and its Applications, vol 137. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-9375-7_5

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  • DOI: https://doi.org/10.1007/978-1-4684-9375-7_5

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