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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.
CitationDreher, M.; Quintanilla, R.; Racke, R. Ill-posed problems in thermomechanics. "Applied mathematics letters", Setembre 2009, vol. 22, núm. 9, p. 1374-1379.
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