The exponential stability property of an evolutionary process is characterized in terms of the existence of some functionals on certain function spaces. Thus are generalized some well-known results obtained by Datko, Rolewicz, Littman and Van Neerven.
The present paper investigates the thermal convection in Walters‘ (model B‘) fluid saturated by a porous medium in the presence of uniform vertical magnetic field. For the porous medium, Brinkman model is employed and Walters‘ (model B‘) fluid model is used to describe the rheological behavior of elastico-viscous fluid. By applying normal mode analysis method, the dispersion relation has been derived and solved analytically. It is observed that the magnetic field and viscoelasticity introduce oscillatory modes. For stationary convection, it is observed that the Walters‘ (model B‘) elastico-viscous fluid behaves like an ordinary Newtonian fluid. The effects of Darcy number, magnetic field and medium permeability have been discussed analytically and numerically in detail. The case of overstability has also been discussed and a sufficient condition for the non-existence of overstability is derived. and Obsahuje seznam literatury, názvosloví a řeckých znaků