Department of Mathematics
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Item type: Item , Access status: Open Access , A nonlinear two phase fluid flow through a porous medium in presence of a well(Springer Nature, 2001-06) Challal, S; Lyaghfouri, AWe study a flow of fresh and salt water in a two dimensional axially symmetric coastal aquifer with a well on the central axis. The flow is governed by a nonlinear Darcy's law. We also show the behaviour of the solution when the out flow of salt water at well goes to 0.Item type: Item , Access status: Open Access , Regularity of the Free Boundary in $div(a(x) \nabla u(x,y) )= -(h(x)\gamma(u))_x$ with $h^\prime (x)<0$(2021-12-15) Challal, SamiaA free boundary problem of type div(a(x)∇u) = −(h(x)γ(u))x with hx < 0 is considered. A regularity of the free boundary as a curve y = Φ(x) is established using a local monotony bux − uy < 0 close to free boundary points.Item type: Item , Access status: Open Access , Continuity of the free boundary in a non-degenerate p-obstacle problem type with monotone solution(Taylor & Francis, 2012-05-22) Challal, S.We prove the continuity of the free boundary for a non-degenerate p-obstacle problem with monotone solution. The proof uses techniques of comparison and the growth of the solution near free boundary points.Item type: Item , Access status: Open Access , Second Order Regularity for the A-Laplace Operator(Springer Nature, 2010-04-22) Challal, Samia; Lyaghfouri, AbdeslemIn this paper we establish second order regularity for the quasilinear elliptic equation ΔAu = f, where ΔA is the so called A-Laplace operator.Item type: Item , Access status: Open Access , Porosity of free boundaries in A-obstacle problems(Elsevier, 2009-04-08) Challal, S; Lyaghfouri, AWe establish the exact growth of the solution of the A-obstacle problem near the free boundary from which we deduce its porosity.Item type: Item , Access status: Open Access , Second order regularity for the p(x)‐Laplace operator(Wiley, 2011-05-13) Challal, S; Lyaghfouri, AIn this paper, we establish second order regularity for the p(x)-Laplace operator. This generalizes classical results known when the function p(x) is equal to some constant p > 1.Item type: Item , Access status: Open Access , On the behavior of the interface separating fresh and salt groundwater in a heterogeneous coastal aquifer(Department of Mathematics, Texas State University, 2003-04-17) Challal, S; Lyaghfouri, AWe consider a flow of fresh and salt groundwater in a two-dimensional heterogeneous horizontal aquifer. Assuming the flow governed by a nonlinear Darcy law and the permeability depending only on the vertical coordinate, we show the existence of a unique monotone solution that increases (resp. decreases) with respect to the salt (resp. fresh) water discharge. For this solution we prove that the free boundary is represented by the graph x = g(z) of a continuous function. Finally we prove a limit behavior at the end points of the interval of definition of g.Item type: Item , Access status: Open Access , Guiding students Towards Success in Calculus via a Focused Assessment Approach(2023-08-09) Challal, SamiaThe purpose of this study is to ascertain the efficiency of a focused assessments approach in improving student experience in calculus.Item type: Item , Access status: Open Access , A viscoelastic fluid flow through mixing grids(ESE - Salento University Publishing, 1999-01-01) Challal, SWe study the asymptotic behaviour of a viscoelastic fluid in a porous medium Ω ε, (ε> 0) obtained by removing from an open set Ω some small obstacles (TVε) IItem type: Item , Access status: Open Access , A stationary flow of fresh and salt groundwater in a heterogeneous coastal aquifer(Unione Matematica Italiana, 2000-06-01) Challal, S; Lyaghfouri, ASi stabilisce l’esistenza e l’unicità di una soluzione monotona per il problema di frontiera libera correlato al flusso stazionare d’acqua dolce e salata intorno ad un acquifero eterogeneo. Si provano la continuità e l’esistenza di un limite asintotico della frontiera libera.Item type: Item , Access status: Open Access , Homogénéisation d'un problème à mémoire instantanée dans un milieu très finement perforé(l'Académie des sciences, 1993) Challal, SamiaOn étudie l'homogénéisation d'un domaine perforé de petits trous occupé par un fluide visqueux, compressible et barotrope. Le problème est de type élasticité à mémoire instantanée. Dans le problème asymptolique un phénomène de mémoire longue apparaît. On traite explicitement le cas des trous sphériques (de rayon acItem type: Item , Access status: Open Access , Regularity results for a quasilinear free boundary problem(Vilnius Gediminas Technical University, 2020-05-13) Challal, Samia; Lyaghfouri, AbdeslemIn this paper we prove local interior and boundary Lipschitz continuity of the solutions of a quasilinear free boundary problem. We also show that the free boundary is the union of graphs of lower semi-continuous functions.Item type: Item , Access status: Open Access , A barrier function for the regularity of the free boundary in $div(a(x) \nabla u )= -(h(x)\gamma)_x$ with $h_x < 0$(https://ijmaa.in/index.php/ijmaa, 2020-05-13) Challal, SamiaA barrier function is compared to the solution of a class of two dimensional problems near a free boundary point. A regularity of the free boundary is established.Item type: Item , Access status: Restricted , Guiding students succeed in Calculus via a math support and a motivational placement test(2021) Challal, SamiaThe purpose of this analysis is to explore how offering some just-in-time remediation; reviewing basic math tools and conducting a test, motivates students in first year math at Glendon College.