Prof. Abdeslem Lyaghfouri


 

Title:  Professor – Mathematics
School: School of Arts & Sciences
Department: Mathematics & Natural Sciences Department
Office:  Bldg. C-17
Phone: Ext. 1162
Email: abdeslem.lyaghfouri@aurak.ac.ae

Dr. Abdeslem Lyaghfouri joined the American University of Ras Al Khaimah in Fall 2014 as an Associate Professor of Mathematics.  He holds a Ph.D in Math- ematics from the University of Zürich, Switzerland. Before joining AURAK, Dr. Lyaghfouri has held several teaching and research positions at different institu- tions in Europe, the Middle East and North America.

The main research area of Dr. Lyaghfouri lies in the analysis of nonlinear partial differential equations.  In addition,  he is interested in translation  of research mathematics  books.  Dr.  Lyaghfouri published  a total of 40 research articles and a book chapter.  One of his achievements was winning  the King Abdullah International Translation Award in Natural Sciences in 2014.

RESEARCH INTEREST & PUBLICATIONS

  1. Papers published in Proceedings
    1. M. Chipot & A. Lyaghfouri :  An existence theorem for an unbounded dam problem with leaky boundary conditions. Proc.  European  Conference on Elliptic  and Parabolic Problems, Pont-`a-Mousson  (June 1994).  Pitman Research Notes in Mathematics. 325, 64-73, (1995).
    2. M. Chipot & A. Lyaghfouri :  On the uniqueness of the solution of the dam problem with leaky boundary conditions. Progress in partial differential equations : the Metz surveys 4. Pitman Research Notes in Mathematics. 345, 175-186, (1996).
  2. Papers published in referred journals
    1. A. Lyaghfouri :  The inhomogeneous dam problem with linear Darcy’s law and Dirichlet boundary conditions.Mathematical Models and Methods in Applied Sciences Vol. 6, No. 8, 1051-1077, (1996).
    2. M. Chipot & A. Lyaghfouri : The dam problem with nonlinear Darcy’s law and leaky boundary conditions. Mathematical Methods in the Applied Sciences Vol. 20, No. 12, 1045-1068, (1997).
    3. S. Challal & A. Lyaghfouri : A stationary flow of fresh and salt groundwa- ter in a coastal aquifer with nonlinear Darcy’s law. Applicable Analysis Vol. 67, 295-312, (1997).
    4. M. Chipot & A. Lyaghfouri : The dam problem with linear Darcy’s law and nonlinear leaky boundary conditions.Advances in Differential Equations Vol. 3, No. 1, 1-50, (1998).
    5. A. Lyaghfouri : On the uniqueness of the solution of a nonlinear filtra- tion problem through a porous medium. Calculus of Variations and Partial Differential Equations Vol. 6, No. 1, 67-94, (1998).
    6. J. Carrillo & A. Lyaghfouri : On the dam problem with nonlinear Darcy’s laws and Dirichlet boundary conditions. Annali della Scuola Normale Superi- ore di Pisa Cl. Sci. (4) Vol. 26, 453-505, (1998).
    7. A. Lyaghfouri : A unified formulation for the dam problem. Rivista di Matematica della Universit`a di Parma. (6) 1, 113-148, (1998).
    8. A. Lyaghfouri : The evolution dam problem with nonlinear Darcy’s law and leaky boundary conditions. Ricerche di Matematica Vol. XLVII,  Fasc. 2, 297-357, (1998).
    9. A. Lyaghfouri :  The evolution dam problem with  nonlinear Darcy’s law and Dirichlet boundary conditions. Portugaliae Mathematica 56 (1), 1-38 (1999).
    10. A. Lyaghfouri : On the uniqueness of the solution of a unified formulation for the boundary conditions in the dam problem. Annali dell’ Universita di Ferrara Sez. VII 45, 91-122 (1999).
    11. J. Carrillo & A. Lyaghfouri : A filtration problem with nonlinear Darcy’s law and generalized boundary conditions.Advances in Differential Equations Vol. 5, No. 4-6, 515-555 (2000).
    12. S. Challal & A. Lyaghfouri : A stationary flow of fresh and salt ground- water in a heterogeneous coastal aquifer.Bollettino della Unione Matematica Italiana (8) no 2, 505-533 (2000).
    13. S. Challal & A. Lyaghfouri : A nonlinear two phase fluid flow through a porous medium in presence of a well. Nonlinear Differential equations and Applications 8, 117-156 (2001).
    14. J. Carrillo, S. Challal & A. Lyaghfouri : A free boundary problem for a flow of fresh and salt groundwater with nonlinear Darcy’s law. Advances in Mathematical Sciences and Applications 12, no. 1, 191-215 (2002).
    15. S. Challal & A. Lyaghfouri : On the Behavior of the Interface Separating Fresh and Salt Groundwater in a Heterogeneous Coastal Aquifer. Electronic Journal of Differential Equations, Vol. 2003, No. 44, pp. 1-27 (2003).
    16. A. Lyaghfouri : A free boundary problem for a fluid flow in a heteroge- neous porous medium. Annali dell’ Universita di Ferrara-Sez.  VII-Sc. Mat., Vol. IL, 209-262 (2003).
    17. S. Challal & A. Lyaghfouri : A Filtration  Problem through a Heteroge- neous Porous Medium. Interfaces and Free Boundaries Vol.  6, No. 1, 55-79 (2004).
    18. A. Lyaghfouri : A Regularity Result for a Heterogeneous Evolution Dam Problem.  Zeitschrift fu¨r  Analysis und ihre Anwendungen,  Vol.  24, No.  1, 149-166 (2005).
    19. S. Challal & A. Lyaghfouri : On the Continuity of the Free Boundary in Problems of type div(a(x)u) = (χ(u)h(x))x1 . Nonlinear Analysis : Theory, Methods & Applications, Vol. 62, No. 2, 283-300 (2005).
    20. S. Challal & A. Lyaghfouri : A New Formulation of the Dam Problem. European Journal of Applied Mathematics, Vol. 16, No. 5, 583-599 (2005).
    21. S. Challal & A. Lyaghfouri : On a class of Free Boundary Problems of type div(a()u) = div(H ()χ(u)).   Differential and Integral Equations, Vol. 19, No. 5, 481-516 (2006).
    22. S. Challal & A. Lyaghfouri :  On the Dam Problem with  Two Fluids Governed by a Nonlinear Darcy’s Law.  Advances in Differential Equations, Vol. 11, No. 8, 841-892 (2006).
    23. S. Challal & A. Lyaghfouri :  Continuity  of the Free Boundary in the Problem ∆p(h(x, y)χ(u))x  with hx  ;?: 0. Applicable Analysis, Vol.  86, No. 9, 1177-1184 (2007).
    24. A. Lyaghfouri : On the Lipschitz Continuity of the Solutions of a Class of Elliptic Free Boundary Problems. Journal of Applied Analysis, Vol. 14, No. 2, 165-181 (2008).
    25. S. Challal & A. Lyaghfouri : Porosity of Free Boundaries in AObstacle Problems. Nonlinear Analysis :  Theory, Methods & Applications, Vol.  70, No. 7, 2772-2778 (2009).
    26. S. Challal & A. Lyaghfouri : Lipschitz Continuity of Solutions of a Free Boundary Problem Involving the p-Laplacian. Journal of Mathematical Anal- ysis and Applications, Vol. 355, No. 2, 700-707 (2009).
    27. S. Challal & A. Lyaghfouri :  H¨older Continuity  of Solutions to the A– Laplace Equation Involving Measures. Communications  in Pure and Applied Analysis. Vol. 8, No. 5, 1577-1583 (2009).
    28. S. Challal & A. Lyaghfouri :  Gradient  Estimates for p(x)-Harmonic Functions. Manuscripta Mathematica. Vol. 131, No. 3-4, 403-414 (2009).
    29. A. Lyaghfouri :  H¨older  Continuity  of p(x)-Superharmonic Functions. Nonlinear Analysis : Theory, Methods & Applications. Vol. 73, No. 8, 2433-2444 (2010).
    30. S. Challal & A. Lyaghfouri : Second Order Regularity for the ALaplace Operator.  Mediterranean Journal of Mathematics. Vol.  7, No.  3, 283-297 (2010).
    31. S. Challal & A. Lyaghfouri :  The Heterogeneous Dam problem with Leaky Boundary Condition. Communications in Pure and Applied Analysis. Vol. 10, No. 1, 93-125 (2011).
    32. A. Lyaghfouri : A Minimum Problem with Free Boundary for the p(x)- Laplace Operator. Advanced Nonlinear Studies. 11, 25-61 (2011).
    33. S. Challal & A. Lyaghfouri : On the Porosity of the Free boundary in the p(x)-Obstacle Problem. Portugaliae Mathematica. Vol.  68, Fasc. 1, 109-123 (2011).
    34. S. Challal & A. Lyaghfouri : Second Order Regularity for the p(x)Laplace Operator. Mathematische Nachrichten. 284, No. 10, 1270-1279 (2011).
    35. S. Challal & A. Lyaghfouri : Removable  sets for Aharmonic functions. Journal for Analysis and its Applications. Vol. 30, No. 4, 421-433 (2011).
    36. S. Challal, A. Lyaghfouri & J. F. Rodrigues : On the A-Obstacle Problem and the Hausdorff Measure of its Free Boundary. Annali di Matematica Pura ed Applicata. 191, 113-165 (2012).
    37. S. Ibrahim & A. Lyaghfouri : Blow-up of solutions of quasilinear hyper- bolic equations. Mathematical Modelling of Natural Phenomena. Vol. 7, No. 2, 66-76 (2012).
    38. A. Lyaghfouri :  Removable sets for H¨older  continuous p(x)-harmonic functions. Analysis and Applications. Vol. 10, No. 2, 199-206 (2012).
    39. S. Challal, A. Lyaghfouri, J. F. Rodrigues & R. Teymurazyan : On the regularity of the free boundary for a class of quasilinear  obstacle problems. Interfaces and Free Boundaries.  16, 359-394 (2014).
    40. A. Lyaghfouri & E. Zaouche :  Lp-continuity  of solutions to parabolic free boundary problems. Electron. J. Diff. Equ., Vol. 2015, No. 184, pp. 1-9 (2015).
    41. A. Lyaghfouri : Porosity of the Free Boundary in the Singular pParabolic Obstacle Problem. Electron. J. Diff. Equ. Accepted.
  3. A Contributed Chapter to a Book 
    • On the Dam Problem. Handbook of Differential Equations:  Stationary Par- tial Differential Equations, Edited by M. Chipot and P. Quittner.  Elsevier- North Holland. Volume 3, Chapter 6, 465-552, 2006.

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