On an instability exhibited by the ballistic-diffusive heat conduction model of Xu and Hu

Christov, I. C.; Jordan, P. M.

doi:10.1098/rspa.2013.0557

Title: On an instability exhibited by the ballistic-diffusive heat conduction model of Xu and Hu

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Abstract

We show that the constitutive relation for the thermal flux proposed by Xu & Hu (2011) admits an unconditional instability. We also highlight the difference between mathematical models containing delay and those that include relaxation effects.

Authors:

Christov, I. C. ^[1]; Jordan, P. M. ^[2]

Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
U.S. Naval Reserch Lab., Stennis Space Center, MS (United States)

Publication Date:: Wed Nov 13 00:00:00 EST 2013

Research Org.:: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1214823

Report Number(s):: LA-UR-13-27984
Journal ID: ISSN 1364-5021

Grant/Contract Number:: AC52-06NA25396

Resource Type:: Accepted Manuscript

Journal Name:: Proceedings of the Royal Society. A. Mathematical, Physical and Engineering Sciences

Additional Journal Information:: Journal Volume: 470; Journal Issue: 2161; Journal ID: ISSN 1364-5021

Publisher:: The Royal Society Publishing

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICS AND COMPUTING; delayed heat equation; Laplace transform; Maxwell–Cattaneo law; unconditional instability

Citation Formats


                    Christov, I. C., and Jordan, P. M. On an instability exhibited by the ballistic-diffusive heat conduction model of Xu and Hu.  United States: N. p., 2013. 
Web.  doi:10.1098/rspa.2013.0557.

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                    Christov, I. C., & Jordan, P. M. On an instability exhibited by the ballistic-diffusive heat conduction model of Xu and Hu.  United States.  https://doi.org/10.1098/rspa.2013.0557

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                    Christov, I. C., and Jordan, P. M. Wed .  
"On an instability exhibited by the ballistic-diffusive heat conduction model of Xu and Hu".  United States.  https://doi.org/10.1098/rspa.2013.0557.  https://www.osti.gov/servlets/purl/1214823.

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@article{osti_1214823,

  title        = {On an instability exhibited by the ballistic-diffusive heat conduction model of Xu and Hu},

  author       = {Christov, I. C. and Jordan, P. M.},

  abstractNote = {We show that the constitutive relation for the thermal flux proposed by Xu & Hu (2011) admits an unconditional instability. We also highlight the difference between mathematical models containing delay and those that include relaxation effects.},

  doi          = {10.1098/rspa.2013.0557},

  journal      = {Proceedings of the Royal Society. A. Mathematical, Physical and Engineering Sciences},

  number       = 2161,

  volume       = 470,

  place        = {United States},

  year         = {Wed Nov 13 00:00:00 EST 2013},

  month        = {Wed Nov 13 00:00:00 EST 2013}

}

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