We consider global attractors of in nite dimensional dynamical systems given by dissipative partial di erential equations u t = u xx + f(x; u; u x ) on the unit interval 0 < x < 1 under separated, linear, dissipative boundary conditions. Global attractors are called orbit equivalent, if there exists a homeomorphism between them which maps orbits to orbits. The global attractor class is the set ...

In this paper we study the dynamics of a Burgers’ type equation (1.1). First, we use a new method called attractor bifurcation introduced by Ma and Wang in [4, 6] to study the bifurcation of Burgers’ type equation out of the trivial solution. For Dirichlet boundary condition, we get pitchfork attractor bifurcation as the parameter λ crosses the first eigenvalue. For periodic boundary condition,...

We prove the existence of a global attractor for the Newton-Boussinesq equation defined in a two-dimensional channel. The asymptotic compactness of the equation is derived by the uniform estimates on the tails of solutions. We also establish the regularity of the global attractor.

In this paper, we consider one-dimensional attractor of a non-autonomous second order strongly damped lattice system with periodic driving force under Neumann boundary condition or periodic boundary condition. We obtain the existence of a global attractor and prove this attractor is homeomorphic to the circle.