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    Decay properties of linear thermoelastic plates: Cattaneo versus Fourier law

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    Type
    Article
    Authors
    Said-Houari, Belkacem
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2011-10-10
    Online Publication Date
    2011-10-10
    Print Publication Date
    2013-02
    Permanent link to this record
    http://hdl.handle.net/10754/562635
    
    Metadata
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    Abstract
    In this article, we investigate the decay properties of the linear thermoelastic plate equations in the whole space for both Fourier and Cattaneo's laws of heat conduction. We point out that while the paradox of infinite propagation speed inherent in Fourier's law is removed by changing to the Cattaneo law, the latter always leads to a loss of regularity of the solution. The main tool used to prove our results is the energy method in the Fourier space together with some integral estimates. We prove the decay estimates for initial data U0 ∈ Hs(ℝ) ∩ L1(ℝ). In addition, by restricting the initial data to U0 ∈ Hs(ℝ) ∩ L1,γ(ℝ) and γ ∈ [0, 1], we can derive faster decay estimates with the decay rate improvement by a factor of t-γ/2. © 2013 Copyright Taylor and Francis Group, LLC.
    Citation
    Said-Houari, B. (2011). Decay properties of linear thermoelastic plates: Cattaneo versus Fourier law. Applicable Analysis, 92(2), 424–440. doi:10.1080/00036811.2011.625015
    Sponsors
    This work has been supported by KAUST.
    Publisher
    Informa UK Limited
    Journal
    Applicable Analysis
    DOI
    10.1080/00036811.2011.625015
    ae974a485f413a2113503eed53cd6c53
    10.1080/00036811.2011.625015
    Scopus Count
    Collections
    Articles; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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