1,720,997 research outputs found
Global nonlinear stability and "cold convection instability" of non-constant porous throughflows, 2D in vertical planes
No full textPorous horizontal layers are considered. A class of non-constant porous throughflows, 2D in vertical planes, is obtained. The global stability conditions
and the "cold convection instability'' conditions are investigated
On the long-time dynamics of nonautonomous predator-prey models with mutual interference
No full textThe longtime behaviour of a nonautonomous bidimensional Hassell predator-prey model with mutual interference is investigated. The existence of an absorbing set in the phase space is shown, and necessary and sufficient conditions guaranteeing the nonlinear, global, asymptotic stability of the positive solutions have been found by using the Liapunov direct method
Global Stability for a binary reaction-diffusion Lotka-Volterra model with ratio-dependent functional response
No full textA reaction-diffusion system modeling the predation between two species is analyzed in the case in which the predators have to search, share and compete for food. The boundedness and uniqueness of the solutions is proved and conditions guaranteeing the global nonlinear asymptotic stability of the positive equilibrium point have been found. These conditions improve those ones present in the existing literature
Convection in multi-component rotating fluid layers via the auxiliary system method
No full textThe onset of thermal convection in a uniformly rotating horizontal layer filled by a Navier-Stokes multi-component fluid mixture, heated from below and salted partly from above and partly from below, is investigated via the new approach named auxiliary system method Rionero (Rend Lincei Mat Appl 25:1-44, 2014). In the free-free case, via the generalization of the Rionero Linearization Principle: "Decay of linear energy for any initial data implies decay of nonlinear energy at any instant" [given in Rionero (Rend Lincei Mat Appl 25:1-44, 2014) in the absence of rotation], it is shown that conditions guaranteeing linear stability of thermal conduction solution guarantee also absence of subcritical instabilities and global exponential asymptotic nonlinear stability. The classical Benard problem is investigated via a procedure different from the celebrated one given in Chandrasekhar (Hydrodynamic and hydromagnetic stability, 1981)
Double diffusive convection in porous media under the action of a magnetic field
No full textThe onset of thermal convection in an electrically conducting fluid saturating a porous medium, uniformly heated from below, salted by one chemical and embedded in an external transverse magnetic field is analyzed. The critical Rayleigh thermal numbers at which steady and Hopf convection can occur, are determined. Sufficient conditions guaranteeing the effective onset of convection via steady or oscillatory state are provided
Onset of convection for ternary fluid mixtures saturating horizontal porous layers with large pores
No full textTernary fluid mixtures saturating horizontal porous layers with large pores, uniformly rotating around the vertical axis, are investigated. The layers are heated from below, salted from above and from below by two salts. The stabilizing effects of both the rotation and Brinkman terms on the conduction solution are analyzed
Coincidence between linear and global nonlinear stability of non-constant throughflows via the Rionero "Auxiliary System Method"
No full textA system modeling fluid motions in horizontal
porous layers, uniformly heated and salted from below, is
analyzed in the case of variable thermal and solutal diffusivities.
The boundedness and uniqueness of solutions are
shown. A class of non-constant throughflows is found and
their stability is analyzed via a new approach. Conditions of
global nonlinear stability, in closed form, are obtained
Instability of Vertical Constant Through Flows in Binary Mixtures in Porous Media with Large Pores
No full textA binary mixture saturating a horizontal porous layer, with large pores and uniformly heated from below, is considered. The instability of a vertical fluid motion (throughflow) when the layer is salted by one salt (either from above or from below) is analyzed. Ultimately boundedness of solutions is proved, via the existence of positively invariant and attractive sets (i.e. absorbing sets). The critical Rayleigh numbers at which steady or oscillatory instability occurs are recovered. Sufficient conditions guaranteeing that a secondary steady motion or a secondary oscillatory motion can be observed after the loss of stability are found. When the layer is salted from above, a condition guaranteeing the occurrence of “cold” instability is determined. Finally, the influence of the velocity module on the increasing/decreasing of the instability thresholds is investigated
Influence of diffusion on the stability of a full Brusselator model
No full textThe classic Brusselator model consists of four reactions involving six components A, B, D, E, X, Y. In a typical run, the final products and are removed instantly, while, the concentrations of the reactants A and B are kept constant. Then, the classic Brusselator model consisting of two equations for the intermediate X and Y is obtained. When the component B is not considered constant, it is added to the mixture and the so-called full Brusselator model is considered. In this paper, the full Brusselator model is studied. In particular, the boundedness of solutions and the effect of diffusion on the linear stability
is analyzed. Moreover, sufficient conditions ensuring that the unique steady state, unstable (stable) in the ODEs system, becomes stable (unstable) in presence of diffusion, are performed and a first nonlinear stability result is obtained
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