Ill-posed problems in thermomechanics

✍ Scribed by Michael Dreher; Ramón Quintanilla; Reinhard Racke

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 380 KB
• Volume: 22
• Category: Article
• ISSN: 0893-9659
• DOI: 10.1016/j.aml.2009.03.010

✦ Synopsis

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.