On Hadamard-type stability of single-integral constitutive equations for viscoelastic liquids (Q1262003)

The Hadamard-type stability of single-integral constitutive equations has been analysed under the assumption of local linear stability and extremely short and fast disturbances. The necessary and sufficient conditions for the global stability are derived for the particular case of time-strain separable equations with instantaneous elasticity. In what follows, the Oldroyd-Lodge, the Kaye-BKZ and the Wagner models are discussed in greater detail. It is shown that the first and second models are globally stable, while the Wagner models are unstable due to their poor relations with thermodynamics. The results presented do not lead to more fundamental conclusions relevant to the proper formulation of constitutive equations; many other models may be analysed in a similar way.