Attractors for non-compact semigroups via energy equations

  title={Attractors for non-compact semigroups via energy equations},
  author={Ioana Moise and Ioana Moise and Ricardo M. S. Rosa and Ricardo M. S. Rosa and Xiaomin Wang},
The energy-equation approach used to prove the existence of the global attractor by establishing the so-called asymptotic compactness property of the semigroup is considered, and a general formulation that can handle a number of weakly damped hyperbolic equations and parabolic equations on either bounded or unbounded spatial domains is presented. As examples, three specific and physically relevant problems are considered, namely the flows of a second-grade fluid, the flows of a Newtonian fluid… 
Infinite Energy Solutions for Dissipative Euler Equations in $${\mathbb{R}^2}$$R2
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Infinite Dimensional Dynamical Systems in Mechanics and Physics Springer Verlag
Contents: General results and concepts on invariant sets and attractors.- Elements of functional analysis.- Attractors of the dissipative evolution equation of the first order in time:
Asymptotic Behavior of Dissipative Systems
Discrete dynamical systems: Limit sets Stability of invariant sets and asymptotically smooth maps Examples of asymptotically smooth maps Dissipativeness and global attractors Dependence on parameters
Geometric Theory of Semilinear Parabolic Equations
Preliminaries.- Examples of nonlinear parabolic equations in physical, biological and engineering problems.- Existence, uniqueness and continuous dependence.- Dynamical systems and liapunov
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We investigate the long-time behaviour of solutions to the Korteweg-de Vries equation with a zero order dissipation and an additional forcing term, when the space variable varies over ℝ, and prove