Amal Alphonse

WIAS, Berlin
 
Welcome to my page. I'm a scientific staff member at the Weierstrass Institute in Berlin, working in the group of Professor Michael Hintermüller.
My research interests include neural networks and learning, variational inequalities and quasi-variational inequalities, nonlinear PDEs, parabolic equations on evolving surfaces and free boundary problems.

Background
Before joining WIAS, I was a postdoctoral research fellow at the University of Warwick, where I also completed my PhD under the supervision of Professor Charles Elliott in the MASDOC doctoral training centre. My PhD examiners were Professor Juan Luis Vázquez and Professor James Robinson.

2016– Weierstrass Institute
2015–2016Postdoctoral research, Mathematics Institute, University of Warwick
2012–2016PhD in Mathematics, University of Warwick
2011–2012Master's in Mathematics, University of Warwick
2007–2011MMath in Mathematics and Computer Science, University of York
Github
Code available here.
Teaching
Details on the course Obstacle problems and optimal control are here.
Publications
Please find the most up-to-date list of my papers on my Google Scholar.

  1. Subdifferentials and penalty approximations of the obstacle problem [pdf]
    with G. Wachsmuth, submitted (2024).
  2. A neural network approach to learning solutions of a class of elliptic variational inequalities [pdf]
    with M. Hintermüller, A. Kister, C. H. Lun and C. Sirotenko, submitted (2024).
  3. A globalized inexact semismooth Newton method for nonsmooth fixed-point equations involving variational inequalities [pdf]
    with C. Christof, M. Hintermüller and I. P. A. Papadopoulos, submitted (2024).
  4. Free boundary limits of coupled bulk-surface models for receptor-ligand interactions on evolving domains [pdf]
    with D. Caetano, C.M. Elliott and C. Venkataraman, submitted (2024).
  5. Minimal and maximal solution maps of elliptic QVIs: penalisation, Lipschitz stability, differentiability and optimal control [pdf]
    with M. Hintermüller, C.N. Rautenberg and G. Wachsmuth, submitted (2023).
  6. Risk-averse optimal control of random elliptic variational inequalities [pdf]
    with C. Geiersbach, M. Hintermüller and T. M. Surowiec, accepted (2022).
  7. Function spaces, time derivatives and compactness for evolving families of Banach spaces with applications to PDEs [pdf]
    with D. Caetano, A. Djurdjevac and C.M. Elliott, accepted in Journal of Differential Equations (2023).
  8. On the differentiability of the minimal and maximal solution maps of elliptic quasi-variational inequalities [pdf]
    with M. Hintermüller and C.N. Rautenberg, J. Math. Anal. Appl. 507(1) Paper No. 125732, 19 (2022).
  9. Optimal control and directional differentiability for elliptic quasi-variational inequalities [pdf]
    with M. Hintermüller and C.N. Rautenberg, Set-Valued Var. Anal. 30(3) (2022).
  10. Stability and sensitivity analysis for quasi-variational inequalities [pdf]
    with M. Hintermüller and C.N. Rautenberg, In: Hintermüller M., Herzog R., Kanzow C., Ulbrich M., Ulbrich S. (eds) Non-smooth and complementarity-based distributed parameter systems---simulation and hierarchical optimization. Internat. Ser. Numer. Math. Birkhäuser/Springer, Cham (2022).
  11. Analysis of a quasi-variational contact problem arising in thermoelasticity [pdf]
    with C. N. Rautenberg and J.F. Rodrigues, Nonlinear Anal. Paper No. 112728, 40 (2022).
  12. Existence, iteration procedures and directional differentiability for parabolic QVIs [pdf]
    with M. Hintermüller and C.N. Rautenberg, Calc. Var. 59, 95 (2020).
  13. Stability of the solution set of quasi-variational inequalities and optimal control [pdf]
    with M. Hintermüller and C.N. Rautenberg, SIAM J. Control Optim., 58(6), 3508–3532 (2020).
  14. Recent trends and views on elliptic quasi-variational inequalities [pdf]
    with M. Hintermüller and C.N. Rautenberg, In: Hintermüller M., Rodrigues J. (eds) Topics in Applied Analysis and Optimisation. CIM Series in Mathematical Sciences. Springer, Cham (2019).
  15. Directional differentiability for elliptic quasi-variational inequalities of obstacle type [pdf]
    with M. Hintermüller and C.N. Rautenberg, Calc. Var. (2019) 58: 39.
  16. A coupled ligand-receptor bulk-surface system on a moving domain: well posedness, regularity and convergence to equilibrium [pdf]
    with C.M. Elliott and J. Terra, SIAM J. Math. Anal., 50(2) (2018), 1544–1592.
  17. Well-posedness of a fractional porous medium equation on an evolving surface [pdf]
    with C.M. Elliott, Nonlinear Anal. 137 (2016), 3–42.
  18. A Stefan problem on an evolving surface [pdf]
    with C.M. Elliott, Phil. Trans. R. Soc. A 373:20140279 (2015).
  19. On some linear parabolic PDEs on moving hypersurfaces [pdf]
    with C.M. Elliott and B. Stinner, Interfaces Free Bound. 17 (2015), 157–187.
  20. An abstract framework for parabolic PDEs on evolving spaces [pdf]
    with C.M. Elliott and B. Stinner, Port. Math. 72 (2015), 1–46.
Contact
You can email me at firstname.surname@wias-berlin.de.