Analysis of the Three Dimensional Heat Conduction in Nano- or Microscale
نویسندگان
چکیده
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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