Analysis of the three dimensional heat conduction in nano- or microscale

H. Heidari, Heiko J. Zwart, Alaeddin Malek

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    Abstract

    The Dual-Phase-Lagging (DPL) equation is formulated as an abstract differential equation. In the absence of a heat source term the DPL equation with homogeneous boundary conditions generates a contraction semigroup. The exact expression of the semigroup is achieved. It is proved that the associated eigenfunctions form a Riesz basis. The stability of semigroup is proved. Moreover, it is also shown that the spectrum of DPL equation contains an interval. This implies that the infinitesimal generator associated to the DPL equation is not a Riesz spectral operator. Therefore, the known test for approximate controllability cannot be used. Several controllability properties are investigated.
    Original languageUndefined
    Title of host publicationProceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2010
    Place of PublicationBudapest
    PublisherEötvös Loránd University
    Pages1877-1882
    Number of pages6
    ISBN (Print)978-963-311-370-7
    Publication statusPublished - Jul 2010
    Event19th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2010 - Budapest, Hungary
    Duration: 5 Jul 20109 Jul 2010
    Conference number: 19

    Publication series

    Name
    PublisherEötvös Loránd University

    Conference

    Conference19th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2010
    Abbreviated titleMTNS
    CountryHungary
    CityBudapest
    Period5/07/109/07/10

    Keywords

    • METIS-277504
    • EWI-19384
    • MSC-93A25
    • IR-75752

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