Abstract
In this paper, we address the model of global attractor formulated in the form of evolution differential inclusions with second order in Banach spaces. Firstly, based on the fixed point theorem, the existence result of mild solutions is deduced. Then, by implementing the measure of noncompactness, the existence of global attractor associated with m -semiflow is validated. Finally, a concrete application of the main result is demonstrated to enhance the practical signification.
Highlights
Consider a Banach space (E, ‖ · ‖)
Semilinear evolution differential inclusions were explored by Cardinali and Rubbioni in [4]
Valero, and Tran et al were devoted to researching on global attractor of multivalued semiflows and differential inclusions, see [7,8,9,10,11,12,13] and references therein
Summary
A set R is said to be a global attractor of Φ, provided that the following conditions are satisfied:. (i) For every t ∈ Γ+, u ⟶ Φ(t, u) is u.s.c. with closed values (ii) Φ has an absorbing set (iii) Φ is asymptotically upper semicompact, i.e., for every bounded B ⊂ E with bounded c(T+()B) for some positive value T(B), any sequence ξn ∈ E: ξn ∈ Φ(tn, B) is relatively compact as tn ⟶ + ∞. 3. The Existence Result of Mild Solutions is section is based on the idea of [3] for nonlinear evolution hemivariational inequalities with second order, which is adapted for evolution differential inclusions in our context. E m-semiflow associated with system (1) is given as follows: Φ: R+ × U ⟶ P(U) Φ(t, ξ) (u(t), u(t)): x is a mild solution of (1.1), ξ u0, v0. It is verified by analogizing the proof of Lemma 3.8 of [8]
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