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

Heidari, Hanif and Zwart, Hans and Malek, Alaeddin (2010) *Controllability and stability of 3D heat conduction equation in a submicroscale thin film.* [Report]

| PDF 181Kb |

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. |

Item Type: | Report |

Faculty: | Electrical Engineering, Mathematics and Computer Science (EEMCS) |

Research Group: | |

Link to this item: | http://purl.utwente.nl/publications/69930 |

Publisher URL: | http://www.math.utwente.nl/publications |

Export this item as: | BibTeX EndNote HTML Citation Reference Manager |

Repository Staff Only: item control page