The paper is devoted to the Cauchy problem for a semilinear damped wave equation in the whole of R^n. Under suitable assumptions a bounded dissipative semigroup of global solutions is constructed in a locally uniform space H[...]^R^n) x L[...](R^n). Asymptotic compactness of this semigroup and the existence of a global attractor are then shown.
In this article, we consider a non-autonomous nonlinear bipolar with phase transition in a two-dimensional bounded domain. We assume that the external force is singularly oscillating and depends on a small parameter ε. We prove the existence of the uniform global attractor Aε. Furthermore, using the method of [9] in the case of the two-dimensional Navier-Stokes systems, we study the convergence of Aε as e goes to zero.
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