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

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:
 [1] ;  [2]
  1. Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  2. U.S. Naval Reserch Lab., Stennis Space Center, MS (United States)
Publication Date:
Report Number(s):
LA-UR-13-27984
Journal ID: ISSN 1364-5021
Grant/Contract Number:
AC52-06NA25396
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
Research Org:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org:
USDOE
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
OSTI Identifier:
1214823