Publications

• Well-posedness theory for a non-conservative Burgers type system arising in dislocation dynamics.
  SIAM Journal on Mathematical Analysis, 39 (2007), pp. 965-986.
   
• A convergent scheme for a non-local coupled system modelling the dynamics of dislocation densities.
  (avec N. Forcadel), Mathematics of Computation, 77 (2008), pp. 789-812.
   
• Derivation and study of dynamical models of dislocation densities.
  (avec H. Ibrahim et R. Monneau), ESAIM: Proceedings, 27 (2009), pp. 227-239.
   
• Global existence for a system of non-linear and non-local transport equations describing the dynamics of dislocation densities.
  (avec M. Cannone, R. Monneau et F. Ribaud), Archive for Rational Mechanics and Analysis, 196 (2010), pp. 71-96.
   
• Dislocation dynamics: from microscopic models to macroscopic crystal plasticity.
  (avec H. Ibrahim et R. Monneau), Continuum Mechanics and Thermodynamics, 21 (2009), pp. 109-123.
   
• Homogenization of dislocation dynamics.
  (avec H. Ibrahim et R. Monneau), Materials Science and Engineering, 3 (2009) 012023.
   
• Short time existence and uniqueness in Hölder spaces for the 2D dynamics of dislocation densities.
  Annales de l'Institut Henri Poincaré (C) Non Linear Analysis, 27 (2011), pp. 21-35.
   
• Global continuous solutions for diagonal hyperbolic systems with large and monotone data.
  (avec R. Monneau), Journal of Hyperbolic Differential Equations, 1 (2012), pp. 1-26.
   
• Hölder stability estimates for some inverse pointwise source problems.
  (avec A. El Badia), C. R. Acad. Sci. Paris Sér. I Math, 350 (2012), pp. 1031-1035
   
• Identification of dislocations in materials from boundary measurements.
  (avec A. El Badia), SIAM Journal on Applied Mathematics, pp. 73-1 (2013), pp. 84-103.
   
• Some uniqueness results for diagonal hyperbolic systems with large and monotone data.
  (avec R. Monneau), Journal of Hyperbolic Differential Equations, 10 (2013), pp. 461-494.
   
• Stability estimates for an inverse source problem of Helmholtz's equation from a single Cauchy data at fixed frequency.
  (avec A. El Badia), Inverse Problems, 29 (2013), 468383.
   
• Reconstruction of extended sources with small supports in the elliptic equation Δu + µu = F from a single Cauchy data.
  (avec B. Abdelaziz et A. El Badia), C. R. Acad. Sci. Paris Sér. I Math, 351 (2013), pp. 797-801.
   
• Identification of pointwise sources in a bioluminescent tomography problem.
  (avec B. Abdelaziz et A. El Badia), ESAIM: Proceedings, 45 (2014), pp. 390-399.
   
• Direct algorithm for multipolar sources reconstruction.
  (avec B. Abdelaziz et A. El Badia), J. Math. Anal. Appl. 428 (2015), pp. 306-336.
   
• Existence result for one-dimensional eikonal equation.
  (avec R. Boudjerada et M. Said Moulay), C. R. Acad. Sci. Paris Sér. I Math, 353 (2015), pp. 133-137.
   
• Global existence result for eikonal equation with BV initial data.
  (avec R. Boudjerada), Nonlinear Differential Equations and Applications, 22, (2015), pp. 947-978.
   
• Direct algorithms for solving some inverse source problems in 2D elliptic equations.
  (avec B. Abdelaziz et A. El Badia), Inverse Problems, 31, (2015), 105002.
   
• Lipschitz stability estimates for an inverse source problem in an elliptic equation from interior measurements.
  (avec A. El Badia, M. Jazar et H. Moustafa), Appl. Anal. 95 (2016), no. 9, pp. 1873-1890.
   
• Some remarks on the small inhomogeneities reconstruction problem.
  (avec B. Abdelaziz et A. El Badia), Inverse Problems and Imaging, 11 (2017), no. 6, pp. 1027-1046.
   
• Logarithmic stability estimates for an inverse source problem from interior measurements.
  (avec A. El Badia, M. Jazar et H. Moustafa), Applicable Analysis, 97 (2018), no. 2, pp. 274-294.
   
• Global BV solution for a non-local coupled system modeling the dynamics of dislocation densities.
  (avec H. Ibrahim et V. Rizik), Journal of Differential Equations, 264 (2018), no. 3, pp. 1750-1785.
   
• Global solution for a non-local eikonal equation modelling dislocation dynamics,
  Nonlinear Analysis, 168 (2018), pp. 154-175.
   
• Identification of point sources in an elliptic equation from interior measurements: Application to a seawater intrusion problem.
  (avec A. El Badia, M. Jazar et H. Moustafa), Journal of Inverse and Ill-posed Problems, 27 (2019), no. 4, pp. 559-574.
   
• The Dirichlet problem for semilinear elliptic equations in an infinite sector.
  (avec H. Ibrahim), Annali di Matematica Pura ed Applicata, 198, (2019), pp. 1551-1561.
   
• Identification of physical parameters in pressing of rapeseeds from the oil flux measurements.
  (avec R. M. Ahmed Bacha, A. El Badia et S. Mottelet), Math. Methods Appl. Sci. 43 (2020), no. 15, 8379-8405.
   
• Existence and uniqueness of continuous solution for a non-local coupled system modeling the dynamics of dislocation densities.
  (avec A. Oussayli), Journal of Nonlinear Science, 31, (2021), pp. 1-41.
   
• Convergence of an implicit scheme for diagonal nonconservative hyperbolic systems.
  (avec R. Boudjerada, A. Oussayli), ESAIM: M2AN 55 (2021) S573-S591.
   
• BV solution for a non-linear Hamilton Jacobi system.
  (avec H. Ibrahim et V. Rizik), Discrete and Continuous Dynamical Systems (A), 41(7), (2021), pp. 3273-3293.
   
• Global existence to a diagonal hyperbolic system for any BV initial data.
  (avec M. Al Zohbi et M. Jazar), Nonlinearity 34 (2021) 5485.
   
• Global discontinuous solution for 1D isentropic gas dynamics system.
  (avec H. Ibrahim et V. Rizik), Communications in Mathematical Sciences, Vol. 19, No. 5 (2021), pp. 1451-1459.
   
• Continuous solution for a non-linear eikonal system.
  (avec A. Oussayli), Communications on Pure & Applied Analysis, 20 (11), (2021), pp. 3795-3823.
   
• Identification of small-sized dislocations using direct algorithm.
  (avec B. Abdelaziz et A. El Badia), Inverse Problems and Imaging, 16 (1), (2022), pp. 197-214.
   
• Convergent semi-explicit scheme to a non-linear eikonal system.
  (avec M. Al Zohbi et M. Jazar), BIT Numerical Mathematics 62, 1841-1872 (2022).
   
• Convergent scheme for a non-local transport system modeling dislocations dynamics.
  (avec A. Oussayli), Journal of Computational and Applied Mathematics 448, (2024), 115929
   
• Existence and uniqueness results to a system of Hamilton-Jacobi equations.
  (avec M. Al Zohbi), accepté dans La Matematica (2024).