Controllability and stability of 3D heat conduction equation in a submicroscale thin film

H. Heidari, Heiko J. Zwart, Alaeddin Malek

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    Abstract

    We obtain a closed form analytic solution for the Dual Phase Lagging equation. This equation is a linear, time-independent partial differential equation modeling the heat distribution in a thin film. The spatial domain is of micrometer and nanometer geometries. We show that the solution is described by a semigroup, and obtain a basis of eigenfunctions. The closure of the set of eigenvalues contains an interval, and so the theory on Riesz spectral operator of Curtain and Zwart cannot be applied directly. The exponential stability and the approximate controllability is shown.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Number of pages21
    Publication statusPublished - Feb 2010

    Publication series

    NameMemorandum / Department of Applied Mathematics
    PublisherDepartment of Applied Mathematics, University of Twente
    No.1917
    ISSN (Print)1874-4850
    ISSN (Electronic)1874-4850

    Keywords

    • IR-69930
    • METIS-277397
    • MSC-35Q80
    • MSC-35Q93
    • MSC-35P10
    • MSC-93B05
    • MSC-74K35
    • EWI-17434
    • Thin film
    • Semigroup
    • Dual phase lagging

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