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

H. Heidari; Heiko J. Zwart; Alaeddin Malek

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

H. Heidari, Heiko J. Zwart, Alaeddin Malek

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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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 language	Undefined
Title of host publication	Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2010
Place of Publication	Budapest
Publisher	Eötvös Loránd University
Pages	1877-1882
Number of pages	6
ISBN (Print)	978-963-311-370-7
Publication status	Published - Jul 2010
Event	19th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2010 - Budapest, Hungary Duration: 5 Jul 2010 → 9 Jul 2010 Conference number: 19

Publication series

Name
Publisher	Eötvös Loránd University

Conference

Conference	19th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2010
Abbreviated title	MTNS
Country/Territory	Hungary
City	Budapest
Period	5/07/10 → 9/07/10

Keywords

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

Access to Document

http://www.conferences.hu/mtns2010/

Cite this

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title = "Analysis of the three dimensional heat conduction in nano- or microscale",

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.",

keywords = "METIS-277504, EWI-19384, MSC-93A25, IR-75752",

author = "H. Heidari and Zwart, {Heiko J.} and Alaeddin Malek",

year = "2010",

month = jul,

language = "Undefined",

isbn = "978-963-311-370-7",

publisher = "E{\"o}tv{\"o}s Lor{\'a}nd University",

pages = "1877--1882",

booktitle = "Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2010",

note = "19th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2010 ; Conference date: 05-07-2010 Through 09-07-2010",

}

Heidari, H, Zwart, HJ & Malek, A 2010, Analysis of the three dimensional heat conduction in nano- or microscale. in Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2010. Eötvös Loránd University, Budapest, pp. 1877-1882, 19th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2010, Budapest, Hungary, 5/07/10. <http://www.conferences.hu/mtns2010/>

Analysis of the three dimensional heat conduction in nano- or microscale. / Heidari, H.; Zwart, Heiko J.; Malek, Alaeddin.
Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2010. Budapest: Eötvös Loránd University, 2010. p. 1877-1882.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - Analysis of the three dimensional heat conduction in nano- or microscale

AU - Heidari, H.

AU - Zwart, Heiko J.

AU - Malek, Alaeddin

N1 - Conference code: 19

PY - 2010/7

Y1 - 2010/7

N2 - 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.

AB - 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.

KW - METIS-277504

KW - EWI-19384

KW - MSC-93A25

KW - IR-75752

M3 - Conference contribution

SN - 978-963-311-370-7

SP - 1877

EP - 1882

BT - Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2010

PB - Eötvös Loránd University

CY - Budapest

T2 - 19th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2010

Y2 - 5 July 2010 through 9 July 2010

ER -