Fachbereich
Mathematik und Statistik
Universität
Konstanz
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Schwerpunkt Analysis und Numerik > Michael Dreher

Ill-posed problems in thermomechanics

M. Dreher, R. Quintanilla and R. Racke

Abstract. 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- 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.

Appl. Math. Lett. 22 (2009), 1374-1379.


The paper is available on request.