Pullback attractor for differential evolution inclusions with infinite delays

Dac, Nguyen Van; Ke, Tran Dinh

doi:10.1016/j.amc.2015.05.092

Cited by 2 publications

(3 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the rest of this section, we introduce some basic results about the pullback attractor and m-process based from [7,11,39,40].…”

Section: Background Materialsmentioning

confidence: 99%

“…if D ∈ D and D ′ ∈ P cl (E) such that D ′ (t) ⊂ D(t) for all t ∈ R, then D ′ ∈ D. From now on D always denotes a Universe and let U : R d × E → P(E) be a m-process. We now collect some basic definition from [7,11,39,40] as follows, with some slight modifications.…”

Section: Background Materialsmentioning

confidence: 99%

“…On the other hand, we note that there is still little information known for the long time behaviour of solutions to the DPHVIs. For this reason, stated as theorem 5.5 in our present paper, we would like to fill a gap and study the existence of a pullback attractor for the multivalued process (m-process) governed by an extension of the DPHVI (1.1)-(1.3) by applying the framework developed in [7,11,39,40], which is the most main novelties in comparison with Migórski and Zeng [32]. The manuscript is structured as follows.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Solvability and pullback attractor for a class of differential hemivariational inequalities with its applications

Li¹,

Liu

Papageorgiou

2023

Nonlinearity

View full text Add to dashboard Cite

In this paper, we consider an abstract system which consists of a nonlinear differential inclusion and a parabolic hemivariational inequality (DPHVI) in Banach spaces. The objective of this paper is four fold. The first target is to deal with the existence of solutions and the properties which involve the boundedness and continuous dependence results of the solution set to parabolic hemivariational inequality. The second aim is to investigate the existence of mild solutions to DPHVI by means of a fixed point technique. The third one is to study the existence of a pullback attractor for the multivalued processes governed by DPHVI. Finally, the fourth goal is to demonstrate a concrete application of our main results arising from the dynamic thermoviscoelasticity problems.

show abstract

“…In the rest of this section, we introduce some basic results about the pullback attractor and m-process based from [7,11,39,40].…”

Section: Background Materialsmentioning

confidence: 99%