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Ill-posed problems in thermomechanics
Dreher, Michael; Quintanilla de Latorre, Ramón; Racke, Reinhard
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II; Universitat Politècnica de Catalunya. GRAA - Grup de Recerca en Anàlisi Aplicada
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.
Peer Reviewed
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències
Heat--Conduction
Stability
Applied mathematics
Estabilitat
Matemàtica aplicada
Calor -- Conducció
info:eu-repo/semantics/publishedVersion
Article
Elsevier
         

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