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


Heidari, Hanif and Zwart, Hans and Malek, Alaeddin (2010) Analysis of the three dimensional heat conduction in nano- or microscale. In: 19th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2010, 5-9 July 2010, Budapest, Hungary (pp. pp. 1877-1882).

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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.
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Electrical Engineering, Mathematics and Computer Science (EEMCS)
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