In this paper, we consider a Cahn-Hillard/Allen-Cahn equation. By using the semigroup and the classical existence theorem of global attractors, we give the existence of the global attractor in H^k(0

in this paper, we consider a cahn-hillard/allen-cahn equation. by using the semigroup and the classical existence theorem of global attractors, we give the existence of the global attractor in h^k(0

The attractor is a central object of an iterated function system (IFS), and fractal transformations are the natural maps from the attractor of one IFS to the attractor of another. This paper presents a global point of view, showing how to extend the domain of a fractal transformation from an attractor with non-empty interior to the ambient space. Intimitely related is the extension of addressin...

The elementary set, or alphabet, of neural firing modes is derived from the widely accepted conductance-based rectified firing-rate model. The firing dynamics of interacting neurons are shown to be governed by a multidimensional bilinear threshold discrete iteration map. The parameter-dependent global attractors of the map morph into 12 attractor types. Consistent with the dynamic modes observe...

In view of the possibility that the 3D Navier-Stokes equations (NSE) might not always have regular solutions, we introduce an abstract framework for studying the asymptotic behavior of multi-valued dissipative evolutionary systems with respect to two topologies—weak and strong. Each such system possesses a global attractor in the weak topology, but not necessarily in the strong. In case the lat...

|In this paper, we study the asymptotic behaviour of the solutions for the Benjamin-Bona-Mahony equation. We rst present the existence of the global weak attractor in H 2 per for this equation. And then by an energy equation we show that the global weak attractor is actually the global strong attractor in H 2 per. In this note, we consider the following Benjamin-Bona-Mahony equation: (1) with t...

Using the theory of uniform global attractors of multivalued semiprocesses, we prove the existence of a uniform global attractor for a nonautonomous semilinear degenerate parabolic equation in which the conditions imposed on the nonlinearity provide the global existence of a weak solution, but not uniqueness. The Kneser property of solutions is also studied, and as a result we obtain the connec...

In a series of recent papers, some of the authors have addressed with mathematical rigor some aspects of the primitive equations governing the large-scale atmospheric motion. Among other results, they derived without evaluating it an expression for the dimension of the attractor for those equations. It is known that the long-term behavior of the motion and states of the atmosphere can be descri...