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Ill-posed problems in thermomechanics

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2009

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Quintanilla, Ramón

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https://doi.org/10.1016/j.aml.2009.03.010
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Applied Mathematics Letters. Elsevier. 2009, 22(9), pp. 1374-1379. ISSN 0893-9659. eISSN 1873-5452. Available under: doi: 10.1016/j.aml.2009.03.010

Zusammenfassung

Several thermomechanical models have been proposed from a heuristic point of view. A mathematical analysis should help to clarify the applicability of these models, among those recent thermal or viscoelastic models. Single-phase-lag and dual-phase-lag heat conduction models can be interpreted as formal expansions of delay equations. The delay equations are shown to be ill-posed, as are the formal expansions of higher order — in contrast to lower-order expansions leading to Fourier’s or Cattaneo’s law. The ill-posedness is proved, showing the lack of continuous dependence on the data, and thus showing that these models (delay or higher-order expansion ones) are highly explosive. In this note we shall present conditions for when this happens.

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510 Mathematik

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ISO 690DREHER, Michael, Ramón QUINTANILLA, Reinhard RACKE, 2009. Ill-posed problems in thermomechanics. In: Applied Mathematics Letters. Elsevier. 2009, 22(9), pp. 1374-1379. ISSN 0893-9659. eISSN 1873-5452. Available under: doi: 10.1016/j.aml.2009.03.010
BibTex
@article{Dreher2009Illpo-58198,
  year={2009},
  doi={10.1016/j.aml.2009.03.010},
  title={Ill-posed problems in thermomechanics},
  number={9},
  volume={22},
  issn={0893-9659},
  journal={Applied Mathematics Letters},
  pages={1374--1379},
  author={Dreher, Michael and Quintanilla, Ramón and Racke, Reinhard}
}
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