Evolutionary problems driven by variational inequalities

Liu, Zhenhai; Zeng, Shengda; Motreanu, Dumitru

doi:10.1016/j.jde.2016.01.012

Cited by 123 publications

(104 citation statements)

References 15 publications

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“…Theorem 3.1 extends the results in Costea and Radulescu [5], Liu and Zeng [18], and Liu et al [19]. Many important situations are incorporated in Theorem 3.1.…”

Section: Properties Of Solution Set For Shvisupporting

confidence: 73%

“…It is worth pointing out that the system (SEDI) of evolutionary differential inclusions includes as a special case the evolutionary differential inclusion (EDI) in [19] because (SEDI) reduces to (EDI) in [19] [19] from problem (EEVI) in [19] to (SEESHVI).…”

Section: The Solution Set Of (Sedi) Is Compact In C([0 T ]; V)mentioning

confidence: 99%

“…Very recently, Liu et al [19] formulated a new type of problems that consists of an evolution equation driven by a variational inequality ((EEVI) for short)     …”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A system of evolutionary problems driven by a system of hemivariational inequalities

Ceng¹,

Wen²,

Yao³

et al. 2018

J. Nonlinear Sci. Appl.

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“…Theorem 3.1 extends the results in Costea and Radulescu [5], Liu and Zeng [18], and Liu et al [19]. Many important situations are incorporated in Theorem 3.1.…”

Section: Properties Of Solution Set For Shvisupporting

confidence: 73%

Section: The Solution Set Of (Sedi) Is Compact In C([0 T ]; V)mentioning

confidence: 99%

See 1 more Smart Citation

A system of evolutionary problems driven by a system of hemivariational inequalities

Ceng¹,

Wen²,

Yao³

et al. 2018

J. Nonlinear Sci. Appl.

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“…On the other hand, the general tangential contact condition (27) with adhesion, i.e., friction contact condition with adhesion, is governed by the subgradient of a nonconvex function j τ . In fact, this contact condition without the bonding field has been treated in many papers, see, e.g., [15,34,35,44,45].…”

Section: Problem 17 Find a Displacement Fieldmentioning

confidence: 99%

“…t ∈ (0, T ). On the other hand, by contact conditions (26), (27), and the definition of the subgradient, we obtain…”

Section: Problem 17 Find a Displacement Fieldmentioning

confidence: 99%

A class of fractional differential hemivariational inequalities with application to contact problem

Zeng

Liu

Migórski

2018

Z. Angew. Math. Phys.

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Abstract. In this paper, we study a class of generalized differential hemivariational inequalities of parabolic type involving the time fractional order derivative operator in Banach spaces. We use the Rothe method combined with surjectivity of multivalued pseudomonotone operators and properties of the Clarke generalized gradient to establish existence of solution to the abstract inequality. As an illustrative application, a frictional quasistatic contact problem for viscoelastic materials with adhesion is investigated, in which the friction and contact conditions are described by the Clarke generalized gradient of nonconvex and nonsmooth functionals, and the constitutive relation is modeled by the fractional Kelvin-Voigt law.Mathematics Subject Classification. 35L15, 35L86, 35L87, 74Hxx, 74M10.

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