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

* **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)](https://epubs.siam.org/doi/abs/10.1137/20M1372093) 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)](https://www.cambridge.org/core/journals/european-journal-of-applied-mathematics/article/strong-wellposedness-and-inverse-identification-problem-of-a-nonlocal-phase-field-tumour-model-with-degenerate-mobilities/238396FC9E8486320205EF519CB1D11A) 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)](https://www.esaim-m2an.org/articles/m2an/abs/2021/02/m2an200086/m2an200086.html) [ArXiv preprint arXiv:2003.12983](http://arxiv.org/pdf/2003.12983.pdf) * **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)](https://www.sciencedirect.com/science/article/pii/S1468121820301103) [ArXiv preprint arxiv:1912.01945](http://arxiv.org/pdf/1912.01945.pdf) * **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)](https://link.springer.com/article/10.1007/s00245-018-9491-z) [ArXiv preprint arxiv:1707.06853](http://arxiv.org/pdf/1707.06853.pdf) * **Convergence of a Robin boundary approximation for a Cahn-Hilliard system with dynamic boundary conditions**. with P. Knopf in [Nonlinearity 33:4191--4235 (2020)](https://iopscience.iop.org/article/10.1088/1361-6544/ab8351) [ArXiv preprint arxiv:1908.06124](http://arxiv.org/pdf/1908.06124.pdf) * **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)](https://www.degruyter.com/view/journals/anona/10/1/article-p24.xml) 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)](https://iopscience.iop.org/article/10.1088/1361-6420/ab6f9f) 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)](https://www.aimsciences.org/article/doi/10.3934/dcds.2020096) [ArXiv preprint arxiv:1902.07020](http://arxiv.org/pdf/1902.07020.pdf) * **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)](https://www.ems-ph.org/journals/show_abstract.php?issn=1463-9963&vol=21&iss=4&rank=4&p403=1) [ArXiv preprint arxiv:1810.12274](http://arxiv.org/pdf/1810.12274.pdf) * **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)](https://epubs.siam.org/doi/abs/10.1137/18M1210034?mobileUi=0) [ArXiv preprint arxiv:1805.03304](http://arxiv.org/pdf/1805.03304.pdf) * **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)](https://www.sciencedirect.com/science/article/abs/pii/S0362546X19300434?via%3Dihub) [ArXiv preprint arxiv:1803.0829](http://arxiv.org/pdf/1803.0829.pdf) * **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)](https://link.springer.com/article/10.1007/s10444-018-9586-8) [ArXiv preprint arxiv:1702.03855](http://arxiv.org/pdf/1702.03855.pdf) * **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)](https://link.springer.com/article/10.1007/s00245-017-9414-4) [ArXiv preprint arxiv:1608.00488](http://arxiv.org/pdf/1608.00488.pdf) * **Cahn-Hlliard inpainting with double obstacle potential**. with H. Garcke and V. Styles in [SIAM J. Imaging Sci., 11(3):2064--2089 (2018)](https://epubs.siam.org/doi/abs/10.1137/18M1165633?journalCode=sjisbi) [ArXiv preprint arxiv:1801.05527](http://arxiv.org/pdf/1801.05527.pdf) * **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)](https://www.intlpress.com/site/pub/pages/journals/items/cms/content/vols/0016/0003/a011/index.php) [ArXiv preprint arxiv:1709.01469](http://arxiv.org/pdf/1709.01469.pdf)