Nonmonotone slip problem for miscible liquids

Migórski, Stanisław; Szafraniec, Paweł

doi:10.1016/j.jmaa.2018.10.078

Cited by 3 publications

References 15 publications

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Hemivariational Inequality for Navier–Stokes Equations: Existence, Dependence, and Optimal Control

Mahdioui

Aadi

Akhlil

2020

Bull. Iran. Math. Soc.

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In this paper we study existence, dependence and optimal control results concerning solutions to a class of hemivariational inequalities for stationary Navier-Stokes equations but without making use of the theory of pseudo-monotone operators. To do so, we consider a classical assumption, due to J. Rauch, which constrains us to make a slight change on the definition of a solution. The Rauch assumption,, although insure the existence of a solution, does not allow the conclusion that the non-convex functional is locally Lipschitz. Moreover, two dependence results are proved, one with respect to changes of the boundary condition and the other with respect to the density of external forces. The later one will be used to prove the existence of an optimal control to the distributed parameter optimal control problem where the control is represented by the external forces.

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Hemivariational Inequality for Navier–Stokes Equations: Existence, Dependence, and Optimal Control

Mahdioui

Aadi

Akhlil

2020

Bull. Iran. Math. Soc.

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Existence and uniqueness of solution to unsteady Darcy-Brinkman problem with Korteweg stress for modelling miscible porous media flow

Kundu,

Maharana,

Mishra

2024

Journal of Mathematical Analysis and Applications

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Well-Posedness of Steady-State Bingham Type System by a Quasi Variational-Hemivariational Approach

Migórski¹,

Dudek²

2023

Mathematical Modelling

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A stationary incompressible Navier-Stokes equation with a nonmonotone slip boundary condition in a bounded domain for a Bingham type fluid is studied. The weak formulation of the fluid problem leads to a new class of elliptic quasi variational-hemivariational inequality with constraints. The boundary condition represents a generalization of the no leak condition, and a multivalued and nonmonotone version of a nonlinear Navier-Fujita frictional slip condition. The analysis provides results on existence and uniqueness of solution to the quasi variational-hemivariational inequality, and on continuous dependence of the solution on the data. The proofs profit from results of nonsmooth analysis, the theory of pseudomonotone operators, and a fixed point argument.

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Nonmonotone slip problem for miscible liquids

Cited by 3 publications

References 15 publications

Hemivariational Inequality for Navier–Stokes Equations: Existence, Dependence, and Optimal Control

Hemivariational Inequality for Navier–Stokes Equations: Existence, Dependence, and Optimal Control

Existence and uniqueness of solution to unsteady Darcy-Brinkman problem with Korteweg stress for modelling miscible porous media flow

Well-Posedness of Steady-State Bingham Type System by a Quasi Variational-Hemivariational Approach

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