In two recent papers, the authors have studied conditions on the relaxation parameters in order to guarantee the stability or instability of solutions for the Taylor approximations to dual-phase-lag and three-phase-lag heat conduction equations. However, for several limit cases relating to the parameters, the kind of stability was unclear. Here, we analyze these limit cases and clarify whether we can expect exponential or slow decay for the solutions. Moreover, rather general well-posedness results for three-phase-lag models are presented. Finally, the exponential stability expected by spectral analysis is rigorously proved exemplarily.
The final publication is available at Springer via http://dx.doi.org/10.1007/s00028-014-0242-6.
CitationBorgmeyer, K.; Quintanilla, R.; Racke, R. Phase-lag heat conduction: decay rates for limit problems and well-posedness. "Journal of evolution equations", 01 Desembre 2014, vol. 14, núm. 4-5, p. 863-884.
All rights reserved. This work is protected by the corresponding intellectual and industrial property rights. Without prejudice to any existing legal exemptions, reproduction, distribution, public communication or transformation of this work are prohibited without permission of the copyright holder. If you wish to make any use of the work not provided for in the law, please contact: email@example.com