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.
