Kamel Hamdache

@article{hamdache_3631,

title = {Asymptotic behavior of thin ferroelectric models},

author = {Kamel Hamdache and Djamila Hamroun},

url = {www.elsevier.com/locate/nonrwa},

year  = {2025},

date = {2025-10-01},

journal = {Nonlinear Analysis-Real World Applications},

volume = {85},

number = {1},

pages = {104379},

abstract = {It was pointed out in Shaw et al. (2000) that the boundary conditions satisfied by the

polarization play an important role in the description of the thin-limit of ferroelectric materials.

In this work we confirm the importance of this choice. In the present work, we consider the

limiting process as the thickness ? of a thin cylinder of R3 goes to 0, and when the polarization

satisfies two different boundary conditions. The first type of boundary conditions leads to an in-

plane model or 2?? 2? configuration while the second one leads to an (in-plane)-(out-of-plane)

model for the displacement and the polarization namely a 2?? 3? configuration. Moreover, the

thin-limit process in both cases induces a change of the Lamé coefficients in the displacement

equation, the coupling coefficient between the displacement and polarization equations, the

double wells potential of the polarization together to a new contribution in the equation of the

out-of-plane component of the polarization for the 2?? 3? model. The techniques used rely on

a rescaling method that penalizes the out-of-plane variable. Uniform bounds with respect to ?

are established, compactness techniques are employed, and the limits of the penalized terms

are identified.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{hamdache_3173,

title = {Time-periodic solutions to heated ferrofluid flow models},

author = {Kamel Hamdache and Djamila Hamroun and Basma Jaffal-Moutarda},

url = {https://doi.org/10.1112/jlms.12990},

year  = {2024},

date = {2024-10-01},

journal = {Journal Of The London Mathematical Society-Second Series},

volume = {110},

number = {4},

pages = {e12990},

abstract = {In this work, we prove the existence of time-periodic solutions to a model describing a ferrofluid flow heated from below. Navier-Stokes equations satisfied by the fluid velocity are coupled to the temperature equation and the magnetostatic equation satisfied by the magnetic potential. The magnetization is assumed to be parallel to the magnetic field and is given by a nonlinear magnetization law generalizing the Langevin law. The proof is based on a semi-Galerkin approximation and regularization methods together with the fixed point method.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{amirat_2247,

title = {Homogenization of ferrofluid flow models in porous media with Langevin magnetization law},

author = {Youcef Amirat and Kamel Hamdache},

url = {https://www.sciencedirect.com/science/article/pii/S0022247X23001324?via%3Dihub},

year  = {2023},

date = {2023-09-01},

journal = {Journal Of Mathematical Analysis And Applications},

volume = {525},

number = {1},

pages = {127129},

abstract = {The paper is concerned with the homogenization of the equations describing the flow of a ferrofluid through a heterogeneous porous medium ? in the presence of an applied magnetic field. We discuss two models where the magnetization M is parallel to the magnetic field H. In the first one M and H satisfy the relation M=?01?fH in ?, where ?0 is a positive constant and 1?f is the characteristic function of ?f (the pore space). In the second model, M and H satisfy the Langevin magnetization law M=MsL(b1|H|)|H|1?fH, where L is the Langevin function given by L(x)=1tanh?x?1x, Ms is the saturation magnetization and b1 is a positive physical constant. The velocity and the pressure satisfy the Stokes equation with a Kelvin magnetic force. We perform the homogenization of the equations of each of the two models. Using the two-scale convergence method, we rigorously derive the homogenized equation for the magnetic potential and determine the asymptotic limit of the magnetization. Then we rigorously derive a Darcy law.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{hamdache_2246,

title = {The Bloch-Torrey limit of a kinetic transport system},

author = {Kamel Hamdache and Djamila Hamroun},

url = {https://link.springer.com/article/10.1007/s00009-023-02328-y#citeas},

year  = {2023},

date = {2023-06-01},

journal = {Mediterranean Journal Of Mathematics},

volume = {20},

number = {3},

pages = {122},

abstract = {This work is devoted to highlighting the diffusion of some models of Kinetic-Bloch system by an asymptotic analysis. The limit of the kinetic equation when using the classical diffusion scaling shows that the magnetization field becomes parallel to the magnetic field. For the limit of the magnetization when we use a second scaling of the kinetic equation, we show that the dynamics of the magnetization is driven by the Bloch-Torrey diffusion equation.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{amirat_1963,

title = {Homogenization of MHD flows in porous media},

author = {Youcef Amirat and Kamel Hamdache and Vladimir V. Shelukhin},

url = {https://doi.org/10.1016/j.jde.2022.08.014},

year  = {2022},

date = {2022-08-01},

journal = {Journal Of Differential Equations},

volume = {339},

number = {339},

pages = {90-133},

abstract = {The paper is concerned with the homogenization of a nonlinear differential system describing the flow of an electrically conducting, incompressible and viscous Newtonian fluid through a periodic porous medium, in the presence of a magnetic field. We introduce a variational formulation of the differential system equipped with boundary conditions. We show the existence of a solution of the variational problem, and derive uniform estimates of the solutions depending on the characteristic parameters of the flow. Using the two-scale convergence method, we rigorously derive a two-scale equation for the two-scale current density, and a two-pressure Stokes system. We derive, in the case of constant magnetic permeability, an explicit relation expressing the macroscopic velocity as a function of the macroscopic Lorentz force, the pressure gradient, the external body force, and the macroscopic current density, via two permeability filtration ten- sors. When the magnetic field is absent, this relation reduces to the Darcy law.

© 2022 Elsevier Inc. All rights reserved.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{hamdache_1579,

title = {Macroscopic limit of the kinetic Bloch equation},

author = {Kamel Hamdache and Djamila Hamroun},

url = {https://www.aimsciences.org/article/doi/10.3934/krm.2021015},

year  = {2021},

date = {2021-06-01},

journal = {Kinetic And Related Models},

volume = {14},

number = {3},

pages = {541-570},

abstract = {This work concerns the existence of solution of the kinetic spinor Boltzmann equation as well as the asymptotic behavior of such solution when ??0, that is when the time relaxation of the spin-flip collisions is very small in comparison to the time relaxation parameter of the collisions with no spin reversal. Due to the lack of regularity of the weak solution, the switching term H?×M? is not stable under the weak convergences. Hence we establish new estimates of the so},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{hamroun_1169,

title = {Existence of large solutions to the Landau-Lifshitz-Bloch equation},

author = {Djamila Hamroun and Kamel Hamdache},

url = {https://www.intlpress.com/site/pub/pages/journals/items/cms/_home/acceptedpapers/index.php},

year  = {2020},

date = {2020-05-14},

journal = {Communications In Mathematical Sciences},

volume = {18},

number = {2},

pages = {487-513},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{hamdache_606,

title = {Weak Solutions to Unsteady and Steady Models of Conductive Magnetic Fluids},

author = {Kamel Hamdache and Djamila Hamroun},

url = {https://link.springer.com/article/10.1007%2Fs00245-018-9505-x},

year  = {2020},

date = {2020-04-01},

journal = {Applied Mathematics And Optimization},

volume = {81},

pages = {479-509},

abstract = {We study a nonlinear coupling system of partial differential equations describing the dynamic of a magnetic fluid with internal rotations. The present mathematical model generalizes those discussed previously in the literature since actually the fluid is electrically conducting inducing additional nonlinearities in the problem and the dynamics of the magnetic field is described by the quasi-static Maxwell equations instead of the usual magnetostatic ones. We prove existence of weak solutions with finite energy first for the unsteady problem then for the steady one.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{hamdache_995,

title = {Asymptotics behaviours for the Landau-Lifshitz-Bloch equation},

author = {Kamel Hamdache and Djamila Hamroun},

url = {https://dergipark.org.tr/tr/pub/atnaa/issue/49323/512065},

year  = {2019},

date = {2019-12-01},

journal = {Advances in the Theory of Nonlinear Analysis and its Applications},

volume = {3},

number = {3},

pages = {174-191},

abstract = {The Landau-Lifshitz-Bloch (LLB) equation is an interpolation between Bloch equation valid for high temperatures and Landau-Lifshitz equation valid for low temperatures. Conversely in this paper, we discuss the behaviours of the solutions of (LLB) equation both as the temperature goes to infinity or 0. Surprisingly in the first case, the behaviour depends also on the scaling of the damping parameter   and the volume exchange parameter a. Three cases are considered and accordingly we get either a linear stationary equation, Bloch equation or Stokes equation. As for the small temperature behaviour, d and a being independent of the temperature, we show that the limit of (LLB) equation is Landau-Lifshitz-Gilbert equation.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{amirat_895,

title = {Weak solutions to stationary equations of heat transfer in a magnetic fluid},

author = {Youcef Amirat and Kamel Hamdache},

url = {https://www.aimsciences.org/article/doi/10.3934/cpaa.2019035},

year  = {2019},

date = {2019-03-01},

journal = {Communications On Pure And Applied Analysis},

volume = {18},

number = {2},

pages = {709-734},

abstract = {We consider the differential system describing the stationary heat transfer in a magnetic fluid in the presence of a heat source and an external magnetic field. The system consists of the stationary incompressible Navier-Stokes equations, the magnetostatic equations and the stationary heat equation. We prove, for the differential system posed in a bounded domain of R3  and equipped with Fourier boundary conditions, the existence of weak solutions by using a regularization of the Kelvin force and the thermal power.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{hamdache_522,

title = {The appearance of memory effects for a conservative system},

author = {Kamel Hamdache and Luc Tartar},

url = {http://www.sciencedirect.com/science/article/pii/S0362546X18301044},

year  = {2018},

date = {2018-04-01},

journal = {Nonlinear Analysis-Theory Methods & Applications},

volume = {177},

pages = {532-542},

abstract = {We adapt and generalize to conservative systems the analysis of a model in Tartar (1989), a sequence of differential equations which in the limit gives an effective equation with a memory effect: our result is obtained under more realistic assumptions concerning the oscillations of the initial data and the coefficients. © 2018 Published by Elsevier Ltd.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{amirat_166,

title = {Stationary solutions of a heated magnetic fluid model},

author = {Youcef Amirat and Kamel Hamdache},

url = {https://www.tandfonline.com/doi/full/10.1080/00036811.2017.1392013},

year  = {2018},

date = {2018-01-01},

journal = {Applicable Analysis},

volume = {97},

number = {16},

pages = {2762-2777},

abstract = {We consider the differential system which describes the steady flow and heat transfer of an incompressible viscous magnetic fluid in the presence of a heat source and an external magnetic field. The system consists of the stationary incompressible Navier-Stokes equations, the magnetostatic equations and the stationary heat equation. We prove, for the differential system posed in a bounded domain of R3 and equipped with boundary conditions, the existence of weak solutions by using regularization of the Kelvin body force, linearization, and the Schauder fixed point theorem.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{amirat_1,

title = {Steady state solutions of ferrofluid flow model},

author = {Youcef Amirat and Kamel Hamdache},

url = {http://aimsciences.org//article/id/a2e59aa5-3139-4991-935d-1fce2bbae304},

year  = {2016},

date = {2016-11-01},

journal = {Communications On Pure And Applied Analysis},

volume = {15},

number = {6},

pages = {2329-2355},

abstract = {We study two models of differential equations for the stationary flow of an incompressible viscous magnetic fluid subjected to an external magnetic field. The first model, called Rosensweig's model, consists of the incompressible Navier-Stokes equations, the angular momentum equation, the magnetization equation of Bloch-Torrey type, and the magnetostatic equations. The second one, called Shliomis model, is obtained by assuming that the angular momentum is given in terms of the magnetic field, the magnetization field and the vorticity. It consists of the incompressible Navier-Stokes equation, the magnetization equation and the magnetostatic equations. We prove, for each of the differential systems posed in a bounded domain of R3 and equipped with boundary conditions, existence of weak solutions by using regularization techniques, linearization and the Schauder fixed point theorem.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{hamdache_49,

title = {Global weak solutions to a model of micropolar fluids with maxwell-cattaneo heat transfer law},

author = {Kamel Hamdache and Djamila Hamroun and Asma Louardani},

url = {http://www.sciencedirect.com/science/article/pii/S0362546X16300529},

year  = {2016},

date = {2016-07-01},

journal = {Nonlinear Analysis-Theory Methods & Applications},

volume = {142},

pages = {69-96},

abstract = {This work is devoted to the study of a system describing the dynamics of a heated micropolar fluid under the action of an applied magnetic field. The heat transfer is subjected to Maxwell-Cattaneo law instead of the usual Fourier law. Thanks to regularization and compactness methods the global existence in time of weak solutions with finite energy has been proved.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{hamdache_48,

title = {Global existence and long time behavior of solutions to a model of ferroelectric materials},

author = {Kamel Hamdache and Djamila Hamroun},

url = {https://www.sciencedirect.com/science/article/abs/pii/S0022247X16001177?via%3Dihub},

year  = {2016},

date = {2016-06-01},

journal = {Journal Of Mathematical Analysis And Applications},

volume = {438},

number = {2},

pages = {668-700},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{gaudiello_341,

title = {A reduced model for the polarization in a ferroelectric thin wire},

author = {Antonio Gaudiello and Kamel Hamdache},

url = {https://link.springer.com/article/10.1007%2Fs00030-015-0348-8},

year  = {2015},

date = {2015-04-01},

journal = {Nodea-Nonlinear Differential Equations And Applications},

volume = {22},

number = {6},

pages = {1883-1896},

abstract = {In this paper, starting from a non-convex and nonlocal 3Dvariational model for the electric polarization in a ferroelectric material, via an asymptotic process we obtain a rigorous 1D-variational model for a thin wire.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{amirat_624,

title = {Strong solutions to the equations of electrically conductive magnetic fluids},

author = {Youcef Amirat and Kamel Hamdache},

url = {http://www.sciencedirect.com/science/article/pii/S0022247X14006209},

year  = {2015},

date = {2015-01-01},

journal = {Journal Of Mathematical Analysis And Applications},

volume = {421},

number = {1},

pages = {75-104},

abstract = {We study the equations of flow of an electrically conductive magnetic fluid, when the fluid is subjected to the action of an external applied magnetic field. The system is formed by the incompressible Navier-Stokes equations, the magnetization relaxation equation of Bloch type and the magnetic induction equation. The system takes into account the Kelvin and Lorentz force densities. We prove the local-in-time existence of the unique strong solution to the system equipped with initial and boundary conditions. We also establish a blow-up criterion for the local strong solution.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{hamdache_1785,

title = {Existence and uniqueness of solutions for the magnetohydrodynamic flow of a second grade fluid},

author = {Kamel Hamdache and Basma Jaffal-Moutarda},

url = {https://www.researchgate.net/publication/258804643_Existence_and_uniqueness_of_solutions_for_the_magnetohydrodynamic_flow_of_a_second_grade_fluid},

year  = {2012},

date = {2012-06-01},

journal = {Mathematical Methods In The Applied Sciences},

volume = {36},

number = {4},

pages = {478-496},

abstract = {In this work, we consider the flow of a second grade fluid in a conducting domain of R3 and in the presence of a magnetic field. When the initial data are of arbitrary size, we prove that the solution of the magnetohydrodynamics problem exists for a small time and is unique. We also show the global existence of solutions for small initial data.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}