Ill-posed problems in thermomechanics

Dreher, Michael; Quintanilla, Ramón; Racke, Reinhard

Ill-posed problems in thermomechanics

Dateien

Zu diesem Dokument gibt es keine Dateien.

Datum

2009

Autor:innen

Dreher, Michael

Quintanilla, Ramón

Racke, Reinhard

DOI (zitierfähiger Link)

https://doi.org/10.1016/j.aml.2009.03.010

Sammlungen

Mathematik und Statistik

Publikationstyp

Zeitschriftenartikel

Publikationsstatus

Published

Erschienen 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

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.

Fachgebiet (DDC)

510 Mathematik

Zitieren

ISO 690

DREHER, 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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Universitätsbibliographie

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Begutachtet

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