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 in an infinite channel past an obstacle, and a weakly damped, forced Korteweg-de Vries equation on the whole line.
I. Moise et al., "Attractors for Non-Compact Semigroups Via Energy Equations," Nonlinearity, vol. 11, no. 5, pp. 1369 - 1393, IOP Publishing; London Mathematical Society, Sep 1998.
The definitive version is available at https://doi.org/10.1088/0951-7715/11/5/012
Mathematics and Statistics
International Standard Serial Number (ISSN)
Article - Journal
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01 Sep 1998