Related papers: Attractors for gradient flows of non convex functi…
The three-dimensional Navier-Stokes-$\alpha$ model for fast rotating geophysical fluids is considered. The Navier-Stokes-$\alpha$ model is a nonlinear dispersive regularization of the exact Navier-Stokes equations obtained by Lagrangian…
We show how the symmetry of attractors of equivariant dynamical systems can be observed by equivariant projections of the phase space. Equivariant projections have long been used, but they can give misleading results if used improperly and…
In this paper, we consider three-dimensional dynamical systems, as for example the Lorenz model. For these systems, we introduce a method for obtaining families of two-dimensional surfaces such that trajectories cross each surface of the…
We prove the existence of a compact, finite dimensional, global attractor for a coupled PDE system comprising a nonlinearly damped semilinear wave equation and a nonlinear system of thermoelastic plate equations, without any mechanical…
We study stochastic Amari-type neural field equations, which are mean-field models for neural activity in the cortex. We prove that under certain assumptions on the coupling kernel, the neural field model can be viewed as a gradient flow in…
In this paper, we consider an autonomous semi-dynamical system driven by semilinear time-nonlocal evolution equations, these type equations are used to describe the Rayleigh-Stokes problem for a non-Newtonain fluid to a generalized second…
The exponential ordering is exploited in the context of non-auto\-no\-mous delay systems, inducing monotone skew-product semiflows under less restrictive conditions than usual. Some dynamical concepts linked to the order, such as…
We study the long-time behaviour of solutions to some classes of fourth-order nonlinear PDEs with non-monotone nonlinearities, which include the Landau--Lifshitz--Baryakhtar (LLBar) equation (with all relevant fields and spin torques) and…
Absorbing ball in $H^{1}(\mho)$ is obtained for the strong solution to the three dimensional viscous moist primitive equations under the natural assumption $Q_{1},Q_{2}\in L^{2}(\mho)$ which is weaker than the assumption $Q_{1},Q_{2}\in…
Using anisotropic hydrodynamics, we examine the existence of early-time attractors of non-conformal systems undergoing Bjorken expansion. In the case of a constant mass, we find that the evolution of the scaled longitudinal pressure is…
In this paper, we consider a damped Navier-Stokes-Bardina model posed on the whole three-dimensional. These equations have an important physical motivation and they arise from some oceanic model. From the mathematical point of view, they…
In this paper, we first prove an abstract theorem on the existence of polynomial attractors and the concrete estimate of their attractive velocity for infinite-dimensional dynamical systems, then apply this theorem to a class of wave…
We extend a recently introduced class of exactly solvable models for recurrent neural networks with competition between 1D nearest neighbour and infinite range information processing. We increase the potential for further frustration and…
In this paper we explore the features of a graph generated by random walkers with nodes that have evolutionary attractiveness and Boltzmann-like transition probabilities that depend both on the euclidean distance between the nodes and on…
We investigate a non-isothermal viscous relaxation of some nonlocal Cahn-Hilliard equations. This perturbation problem generates a family of solution operators, exhibiting dissipation and conservation. The solution operators admit a family…
The large time behavior of the deterministic and stochastic three dimensional convective Brinkman-Forchheimer (CBF) equations for $r\geq3$ ($r>3$, for any $\mu$ and $\beta$, and $r=3$ for $2\beta\mu\geq1$), in periodic domains is carried…
We prove that the weakly damped nonlinear Schr\"odinger flow in $L^2(\mathbb{R})$ provides a dynamical system which possesses a global attractor. The proof relies on the continuity of the Schr\"odinger flow for the weak topology in…
In this article, we study the long time behavior of solutions of a variant of the Boussinesq system in which the equation for the velocity is parabolic while the equation for the temperature is hyperbolic. We prove that the system has a…
Constrained gradient flows are studied in fracture mechanics to describe strongly irreversible (or unidirectional) evolution of cracks. The present paper is devoted to a study on the long-time behavior of non-compact orbits of such…
We present a comprehensive, nonperturbative analytical method to investigate the dynamics of time-dependent oscillating scalar field configurations. The method is applied to oscillons in a double well Klein-Gordon model in two and three…