Department of Mathematics
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Browsing Department of Mathematics by Subject "Applied mathematics"
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Item 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 Open Access On the regularity of the free boundary for quasilinear obstacle problems(European Mathematical Society - EMS - Publishing House, 2014-09-19) Challal, Samia; Lyaghfouri, Abdeslem; Rodrigues, José Francisco; Teymurazyan, RafayelWe extend basic regularity of the free boundary of the obstacle problem to some classes of heterogeneous quasilinear elliptic operators with variable growth that includes, in particular, the p(x)-Laplacian. Under the assumption of Lipschitz continuity of the order of the power growth p(x) > 1, we use the growth rate of the solution near the free boundary to obtain its porosity, which implies that the free boundary is of Lebesgue measure zero for p(x)-Laplacian type heterogeneous obstacle problems. Under additional assumptions on the operator heterogeneities and on data we show, in two different cases, that up to a negligible singular set of null perimeter the free boundary is the union of at most a countable family of C1 hypersurfaces: (i) by extending directly the finiteness of the (n - 1)-dimensional Hausdorff measure of the free boundary to the case of heterogeneous p-Laplacian type operators with constant p, 1 < p < ∞; (ii) by proving the characteristic function of the coincidence set is of bounded variation in the case of non degenerate or non singular operators with variable power growth p(x) > 1.Item 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 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.