Current Research Interests

Phase field models, mathematical modelling, analysis of partial differential equations, optimal control, inverse problems.

 

 

Selected Publications

• Sparse optimal control of a phase field tumour model with mechanical effects
  with H. Garcke and A. Signori
  SIAM J. Control. Optim., 59:1555-1580 (2021)
  Open access


• Strong well-posedness and inverse identification problem of a non-local phase field tumor model with degenerate mobilities
  with S. Frigeri and A. Signori
  in European Jnl. Appl. Math. (2021)
  Open access


• Phase-field dynamics with transfer of materials: The Cahn-Hillard equation with reaction rate dependent dynamic boundary conditions
  with P. Knopf, C. Liu and S. Metzger
  in ESAIM: M2AN, 55:229-282 (2021)
  ArXiv preprint arXiv:2003.12983


• On a phase field model of Cahn-Hilliard type for tumour growth with mechanical effects.
  with H. Garcke and A. Signori
  in Nonlinear Anal. Real World Appl., 57:103192 (2021)
  ArXiv preprint arxiv:1912.01945


• Parameter identification via optimal control for a Cahn-Hilliard-chemotaxis system with a variable mobility.
  with C. Kahle
  in Appl. Math. Optim., 82:63--104 (2020)
  ArXiv preprint arxiv:1707.06853


• Convergence of a Robin boundary approximation for a Cahn-Hilliard system with dynamic boundary conditions.
  with P. Knopf
  in Nonlinearity 33:4191--4235 (2020)
  ArXiv preprint arxiv:1908.06124


• Weak and stationary solutions to a Cahn-Hilliard-Brinkman model with singular potentials and source terms.
  with M. Ebenbeck
  in Adv. Nonlinear Anal., 10:24--65 (2020)
  Open access


• Consistency of a phase field regularization for an inverse problem governed by a quasilinear Maxwell system.
  with I. Yousept
  in Inverse Problems, 36 (2020) 045011 (33pp)
  Open access


• Convergence to equilibrium for a bulk-surface Allen-Cahn system coupled through a Robin boundary condition.
  with H. Wu
  in Discrete Contin. Dyn. Syst., 40:147--1878 (2020)
  ArXiv preprint arxiv:1902.07020


• Phase field modelling of surfactants in multi-phase flow.
  with O.R.A. Dunbar and B. Stinner
  in Interface Free Bound., 21:495--547 (2019)
  ArXiv preprint arxiv:1810.12274


• Bayesian parameter identification in Cahn-Hilliard models for biological growth.
  with C. Kahle, J. Latz and E. Ullmann
  in SIAM/ASA J. Uncertainty Quantification, 7:526--552 (2019)
  ArXiv preprint arxiv:1805.03304


• On a coupled bulk-surface Allen-Cahn system with non-trivial transmission condition and its approximation by a Robin boundary condition.
  with P. Colli and T. Fukao
  in Nonlinear Anal., 184:116--147 (2019)
  ArXiv preprint arxiv:1803.0829


• A phase field approach to shape optimization in Navier--Stokes flow with integral state constraint.
  with H. Garcke, M. Hinze and C. Kahle
  in Adv. Comput. Math., 44(5):1345--1383 (2018)
  ArXiv preprint arxiv:1702.03855


• Optimal control of treatment time in a diffuse interface model of tumor growth.
  with H. Garcke and E. Rocca
  in Appl. Math. Optim., 78:495--544 (2018)
  ArXiv preprint arxiv:1608.00488


• Cahn-Hlliard inpainting with double obstacle potential.
  with H. Garcke and V. Styles
  in SIAM J. Imaging Sci., 11(3):2064--2089 (2018)
  ArXiv preprint arxiv:1801.05527


• On a multi-species Cahn-Hilliard-Darcy tumor growth model with singular potentials.
  with S. Frigeri, E. Rocca and G. Schimperna
  in Commun. Math. Sci., 16(3):821--856 (2018)
  ArXiv preprint arxiv:1709.01469