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A reaction–diffusion ecoepidemic model of predator–prey type with a transmissible disease spreading among the predator species only is considered. The longtime behavior of solutions is analyzed and, in particular, absorbing sets in the phase space are determined. Conditions guaranteeing the non existence of non-constant equilibria have been found. Linear and non-linear stability conditions for biologically meaningful equilibria are determined. [ABSTRACT FROM AUTHOR]

Abstract: Non-linear stability of vertical throughflows in porous layers, uniformly heated and salted from below, is analyzed. The definitively boundedness of the solutions (existence of absorbing sets in the phase space) is proved. Conditions guaranteeing global non-linear asymptotic stability have been found. In closed form, the critical Rayleigh number has been found. [Copyright &y& Elsevier]

Abstract: The long-time behavior of triply fluid mixtures saturating horizontal porous layers uniformly rotating around the vertical axis, according to the Brinkman law (holding for large pores), is investigated. The most destabilizing case of layers heated from below and salted from above by two salts, is considered. The ultimately boundedness of the solutions (existence of absorbing sets) is shown. A necessary and sufficient condition guaranteeing the global non-linear asymptotic -stability of the conduction solution is obtained. [Copyright &y& Elsevier]

The onset of convection in anisotropic porous medium in local thermal non-equilibrium regime is studied. The Cattaneo's law to describe heat propagation in solid phase is allowed, while the Fourier's law in fluid phase is employed. Linear and nonlinear stability of the conduction solution are performed and the critical Rayleigh numbers in a closed form are obtained. The influence of second sound effect, inter-phase heat transfer and anisotropy of the medium on the onset of instability have been analysed via numerical simulations, too. • The influence of Cattaneo's law on the onset of convection is highlighted. • Conditions for the onset of steady and oscillatory convection have been determined. • The influence of inter-phase heat transfer and Darcy number on convection is analysed • Nonlinear stability analysis with respect to L 2-norm has been performed. [ABSTRACT FROM AUTHOR]

In the present article, a model for penetrative convection in a fluid-saturated inclined porous medium is analyzed. Penetrative convection occurs when an unstably stratified fluid moves into a stably stratified region. In this study, it will be shown that the inclination of the layer plays a relevant role for the penetrative thermal convection of a fluid-saturated porous medium. The results reported in the literature for the limiting case of horizontal layer are recovered and the numerical results for the linear instability, obtained via the Chebyshev- τ method, show that the most destabilizing perturbations are the longitudinal and, as expected, the transverse ones destabilize only up to a certain critical inclination angle of the layer. Moreover, in the numerical analysis of the three-dimensional perturbations, we show that the longitudinal perturbations are the most destabilizing not only with respect to the transverse but also with respect to any general perturbation. We also give nonlinear stability results for the longitudinal perturbations via the weighted energy method. • Influence of upper layer temperature on penetrative convection is highlighted. • Most destabilizing effect of the longitudinal perturbations is found. • Critical inclination angle for transverse perturbations is determined. • Conditions for the onset of steady convection are provided. • Global nonlinear stability analysis of conduction solution has been performed. [ABSTRACT FROM AUTHOR]