Ill-posed problems in thermomechanics

Dreher, Michael; Quintanilla, Ramón; Racke, Reinhard

Ill-posed problems in thermomechanics

Dateien

research_paper_248.pdfGröße: 643.07 KBDownloads: 233

Datum

2008

Autor:innen

Dreher, Michael

Quintanilla, Ramón

Racke, Reinhard

Open Access-Veröffentlichung

Open Access Green

Sammlungen

Mathematik und Statistik

Publikationstyp

Working Paper/Technical Report

Publikationsstatus

Published

Zusammenfassung

In the literature there exist several thermomechanical models which are proposed from a heuristic point of view. A mathematical analysis should help to clarify the applicability of these models. In recent years several thermal or viscoelastic models have been proposed in which the relaxation time or the delay time plays an important role. Single- 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 well as 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, thus showing that these models (delay, or higher-order expansions) are highly explosive. In this note we shall present conditions when this happens.

Fachgebiet (DDC)

510 Mathematik

Zitieren

ISO 690

DREHER, Michael, Ramón QUINTANILLA, Reinhard RACKE, 2008. Ill-posed problems in thermomechanics

BibTex

@techreport{Dreher2008Illpo-636,
  year={2008},
  series={Konstanzer Schriften in Mathematik und Informatik},
  title={Ill-posed problems in thermomechanics},
  number={248},
  author={Dreher, Michael and Quintanilla, Ramón and Racke, Reinhard}
}

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Universitätsbibliographie

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