In this paper we study the heat transfer with a general fractional diffusion term of an incompressible fluid in a porous medium governed by Darcy’s law. We show formation of singularities with infinite energy and for finite energy we obtain existence and uniqueness results of strong solutions for the sub-critical and critical cases. We prove global existence of weak solutions for different case...

Double crises of chaotic oscillators in the presence of fuzzy uncertainty are studied by means of the fuzzy generalized cellmappingmethod.A fuzzy chaotic attractor is characterized by its global topology and membership distribution. A fuzzy crisis implies a simultaneous sudden change both in the topology of the chaotic attractor and in its membership distribution. It happenswhen a fuzzy chaotic...

A nonlinear transmisson problem for an elastic full von Karman beam is considered here. We prove that the system possesses a compact global attractor.

We investigate a system of partial differential equations of reaction-diffusion type which displays propagation of bursting oscillations. This system represents the time evolution of an assembly of cells constituted by a small nucleus of bursting cells near the origin immersed in the middle of excitable cells. We show that this system displays a global attractor in an appropriated functional sp...

Food chain models of ordinary differential equations (ode's) are often used in ecology to gain insight in the dynamics of populations of species, and the interactions of these species with each other and their environment. One powerful analysis technique is bifurcation analysis, focusing on the changes in long-term (asymptotic) behaviour under parameter variation. For the detection of local bif...

In order to study the longtime behavior of a dissipative evolutionary equation, we generally aim to show that the dynamics of the equation is finite dimensional for long time. In fact, one possible way to express this fact is to prove that dynamical systems describing the evolutional equation comprise the existence of the global attractor 1 . The KDV equation without dissipative and forcing was...

We study the effects of large diffusivity in all parts of the domain in a linearly damped wave equation subject to standard zero Robin-type boundary conditions. In the linear case, we show in a given sense that the asymptotic behaviour of solutions verifies a second-order ordinary differential equation. In the semilinear case, under suitable dissipative assumptions on the nonlinear term, we pro...

The viscous Cahn-Hilliard equation arises as a singular limit of the phase-eld model of phase transitions. It contains both the Cahn-Hilliard and Allen-Cahn equations as particular limits. The equation is in gradient form and possesses a compact global attractor A, comprising heteroclinic orbits between equilibria. Two classes of computation are described. First heteroclinic orbits on the globa...

Vibration signals were measured in a lab-scale fluidized bed to investigate the changes in particle sizes. Experiments were carried out in the bed with a different mass fraction of coarser particles at different superficial gas velocities, and probe heights. The S-statistic test evaluates the dimensionless squared distance between two attractors reconstructed from time series of vibration signa...

For autonomous Lotka-Volterra systems modelling the dynamics of N competing species, a new condition has been found to prevent a particular species from dying out. Based on this condition, criteria have been established for all or some of the N species to stabilise at a steady state whilst the others, if any, die out.