I am a post-doc at the Weierstraß Institute for Applied Analysis and Stochastics, Berlin, and member of the research group Partial Differential Equations of Alexander Mielke.

I am also a member of the Berlin Mathematical School (BMS) in the Postdoctoral Faculty.

Together with Annegret Glitzky I am head of the MATH+ project AA2-1 Hybrid models for the electrothermal behavior of organic semiconductor devices.

I have been awarded the ISIMM Junior Prize 2018 at STAMM conference "Mathematics & Mechanics: Natural Philosophy in the 21st Century" in Oxford.

E-mail Matthias.Liero-please remove this text-@wias-berlin.de (Public Key)
Phone +49 (0) 30 20372 542
Fax +49 (0) 30 20372 311


In the summer term SS2018 I am giving a lecture on Mehrdimensionale Variationsrechnung at Humboldt Universität zu Berlin, Tuesdays from 1pm and Thursdays from 9am. The tutorial is on Tuesday from 3pm.

In the winter term WS2017/18 I was giving a lecture on Optimal transport and Wasserstein gradient flows at Humboldt Universität zu Berlin, Tuesdays from 9am.

Research interests

My mathematical expertise is in the field of nonlinear partial differential equations. In particular, the rigorous derivation of new effective models in various problems in natural sciences using novel mathematical techniques is one of my major interests. In my diploma I gave a rigorous justification of an evolutionary elastoplastic plate model for continuum mechanics using the notion of Gamma-convergence. In a joint work with U. Stefanelli (Vienna), we extended the Weighted-Energy-Dissipation principle from parabolic to hyperbolic equations to make them accessible to variational methods.

In the recent years, the mathematical modeling, analysis, and simulation of optoelectronic devices, such as solar cells and organic light-emitting diodes, has become an essential application for me. I work closely with my colleagues Annegret Glitzky, Thomas Koprucki, Jürgen Fuhrmann, and Duy-Hai Doan from WIAS on organic devices. In a joint work with the Dresden Integrated Center for Applied Physics and Photonic Materials, in particular with Axel Fischer, Reinhard Scholz and Sebastian Reineke, we derived a novel PDE model, involving the p(x)-Laplacian with discontinuous p(x), to describe the current and heat flow in organic light-emitting diodes. This was the first model to correctly predict S-shaped current-voltage characteristics with regions of negative differential resistance as observed in measurements.

Moreover, with Michael Sawatzki and Hans Kleemann from IAPP we investigate the behavior and new concepts of organic transistors.

However, also the more abstract theory behind partial differential equations is in the focus of my current work. One particular highlight of a recent joint work with Alexander Mielke (WIAS Berlin) and Giuseppe Savaré (Pavia) was the derivation and characterization of the so-called Hellinger-Kantorovich distance, which can be seen as a generalization of the famous Wasserstein distance to arbitrary measures.

In general, my scientific work is guided by the aim to strengthen the cooperation between analysis and its applications by inventing and further developing the mathematical foundations and techniques to make them applicable for practical questions in other sciences.


I have been involved in the following projects:


  1. Sebastian Reineke, Anton Kirch, Fischer, Matthias Liero, Jürgen Fuhrmann, Annegret GlitzkyExperimental proof of Joule heating-induced switched-back regions in OLEDsaccepted in Light: Science & Applications2020.
  2. Annegret Glitzky, Matthias LieroInstationary drift-diffusion problems with Gauss–Fermi statistics and field-dependent mobility for organic semiconductor devicesComm. Math. Sci.1733–592019.
  3. Annegret Glitzky, Matthias Liero, Grigor NikaAn existence result for a class of electrothermal drift-diffusion models with Gauss–Fermi statistics for organic semiconductor devicesWIAS-Preprint25932019.
  4. Duy Hai Doan, Annegret Glitzky, Matthias LieroAnalysis of a drift-diffusion model for organic semiconductor devicesZ. Angew. Math. Phys.70552019.
  5. Matthias Liero, Stefano MelchionnaThe weighted energy-dissipation principle and evolutionary Γ-convergence for doubly nonlinear problemsESAIM Control Optim. Calc. Var.25362019. (Link)
  6. Yichu Zheng, Axel Fischer, Michael Sawatzki, Duy Hai Doan, Matthias Liero, Annegret Glitzky, Sebastian Reineke, Stefan C. B. MannsfeldIntroducing pinMOS Memory: A Novel, Nonvolatile Organic Memory DeviceAdvanced Functional Materialsn/a19071192019. (Link)
  7. Annegret Glitzky, Matthias Liero, Grigor NikaAnalysis of a hybrid model for the electro-thermal behavior of semiconductor heterostructuresWIAS-Preprint26362019.
  8. Duy Hai Doan, Axel Fischer, Jürgen Fuhrmann, Annegret Glitzky, Matthias LieroDrift-diffusion simulation of S-shaped current-voltage relations for organic semiconductor devicesWIAS-Preprint26302019.
  9. Thomas Frenzel, Matthias LieroEffective diffusion in thin structures via generalized gradient systems and EDP-convergenceWIAS-Preprint26012019.
  10. Karoline Disser, Matthias Liero, Jonathan ZinslEvolutionary Γ-convergence of gradient systems modeling slow and fast chemical reactionsNonlinearity313689–37062018. (Link)
  11. Matthias Liero, Alexander Mielke, Giuseppe SavaréOptimal Entropy-Transport problems and a new Hellinger–Kantorovich distance between positive measuresInventiones mathematicae211969–11172018. (Link)
  12. Franz Michael Sawatzki, Duy Hai Doan, Hans Kleemann, Matthias Liero, Annegret Glitzky, Thomas Koprucki, Karl LeoBalance of Horizontal and Vertical Charge Transport in Organic Field-Effect TransistorsPhys. Rev. Applied100340692018. (Link)
  13. Axel Fischer, Manuel Pfalz, Koen Vandewal, Simone Lenk, Matthias Liero, Annegret Glitzky, Sebastian ReinekeFull Electrothermal OLED Model Including Nonlinear Self-heating EffectsPhys. Rev. Applied100140232018. (Link)
  14. Matthias Liero, Sina ReicheltHomogenization of Cahn–Hilliard-type equations via evolutionary Γ-convergenceNonlinear Differential Equations and Applications NoDEA2562018. (Link)
  15. Jürgen Fuhrmann, Annegret Glitzky, Matthias LieroHybrid Finite-Volume/Finite-Element Schemes for p(x)-Laplace Thermistor ModelsIn: Clément Cancès, Pascal Omnes (eds.) Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems: FVCA 8, Lille, France, June 2017397–4052017.
  16. Matthias Liero, Jürgen Fuhrmann, Annegret Glitzky, Thomas Koprucki, Axel Fischer, Sebastian Reineke3D electrothermal simulations of organic LEDs showing negative differential resistanceOpt. Quantum Electron.49330/1–330/82017.
  17. Miroslav Bulíček, Annegret Glitzky, Matthias LieroThermistor systems of p(x)-Laplace-type with discontinuous exponents via entropy solutionsDiscr. Cont. Dynam. Systems Ser.~S10697–7132017.
  18. Matthias Liero, Alexander Mielke, Mark A. Peletier, D. R. Michiel RengerOn microscopic origins of generalized gradient structuresDiscr. Cont. Dynam. Systems Ser.~S1012017. (Link)
  19. Annegret Glitzky, Matthias LieroAnalysis of p(x)-Laplace thermistor models describing the electrothermal behavior of organic semiconductor devicesNonlinear Analysis: Real World Applications34536–5622017. (Link)
  20. Matthias Liero, Axel Fischer, Jürgen Fuhrmann, Thomas Koprucki, Annegret GlitzkyA PDE Model for Electrothermal Feedback in Organic Semiconductor DevicesProgress in Industrial Mathematics at ECMI 201699–1062017.
  21. Matthias Liero, Jürgen Fuhrmann, Annegret Glitzky, Thomas Koprucki, Axel Fischer, Sebastian ReinekeModeling and Simulation of Electrothermal Feedback in Large-area Organic LEDsProceedings of the 17th International Conference on Numerical Simulation of Optoelectronic Devices, NUSOD 2017105–1062017.
  22. Matthias LieroThe Hellinger-Kantorovich distance as a generalization of optimal-transport distances to scalar reaction-diffusion problemsOberwolfach Rep. 1447–502017.
  23. Miroslav Bulíček, Annegret Glitzky, Matthias LieroSystems describing electrothermal effects with p(x)-Laplace like structure for discontinuous variable exponentsSIAM J. Math. Analysis483496–35142016.
  24. Adrien Bercegol, Binoy Chacko, Reiner Klenk, Iver Lauermann, Martha Ch. Lux-Steiner, Matthias LieroPoint contacts at the copper-indium-gallium-selenide interface–A theoretical outlookJournal of Applied Physics1191553042016. (Link)
  25. Matthias Liero, Alexander Mielke, Giuseppe SavaréOptimal Transport in Competition with Reaction: The Hellinger–Kantorovich Distance and Geodesic CurvesSIAM Journal on Mathematical Analysis482869–29112016. (Link)
  26. Matthias Liero, Thomas Koprucki, Axel Fischer, Reinhard Scholz, Annegret Glitzkyp-Laplace thermistor modeling of electrothermal feedback in organic semiconductor devicesZ. Angew. Math. Phys.662957–29772015.
  27. Karoline Disser, Matthias LieroOn gradient structures for Markov chains and the passage to Wasserstein gradient flowsNetworks & Heterogeneous Media10233–2532015. (Link)
  28. Matthias Liero, Alexander MielkeGradient structures and geodesic convexity for reaction-diffusion systemsPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences371201203462013. (Link)
  29. Matthias LieroPassing from bulk to bulk-surface evolution in the Allen–Cahn equationNonlinear Differential Equations and Applications NoDEA20919–9422013. (Link)
  30. Matthias Liero, Ulisse StefanelliA new minimum principle for Lagrangian mechanicsJ. Nonlinear Sci.23179–2042013.
  31. Matthias Liero, Ulisse StefanelliWeighted inertia-dissipation-energy functionals for semilinear equationsBoll. Unione Mat. Ital. (9)61–272013.
  32. Matthias Liero, Thomas RocheRigorous derivation of a plate theory in linear elastoplasticity via Γ-convergenceNonlinear Differential Equations and Applications NoDEA19437–4572012. (Link)
  33. Matthias Liero, Alexander MielkeAn evolutionary elastoplastic plate model derived via Γ-convergenceMath. Models Meth. Appl. Sci. (M$^3$AS)211961–19862011.
  34. Pavel Krejčí, Matthias LieroRate independent Kurzweil processesApplications of Mathematics54117–1452009. (Link)
  35. Hannelore Liero, Matthias LieroTesting the Acceleration Function in Lifetime ModelsIn: Filia Vonta, Mikhail Nikulin, Nikolaos Limnios, Catherine Huber-Carol (eds.) Statistical Models and Methods for Biomedical and Technical Systems225–2392008. (Link)

Short CV

1982Born in Berlin, Germany
2002 Abitur, Carl-von-Ossietzky Gymnasium, Berlin
2002 -- 2003Civilian service, Charité Berlin
2003 -- 2008Study of Mathematics (minor in Physics) at Humboldt-Universität zu Berlin, Diploma Thesis: Herleitung eines elastoplastischen Plattenmodells mit Methoden der Γ-Konvergenz (supervisor: Prof. Dr. Alexander Mielke)
2006 -- 2007Student assistant at WIAS Berlin, Research Group Thermodynamic Modeling and Analysis of Phase Transitions
2008 -- 2010 PhD student in DFG Research Training Group 1128 Analysis, Numerics, and Optimization of Multiphase Problems
Feb 2010 -- Jul 2010 Research period at I.M.A.T.I. Pavia, funded by BioSMA research programme (supervisor: Prof. Dr. Ulisse Stefanelli)
Aug 2010 -- Dec 2012 PhD student at WIAS Berlin, MATHEON project D22: Modeling of Electronic Properties of Interfaces in Solar Cells
Dec 2012 Defense of PhD thesis at Humboldt-Universität zu Berlin: Variational Methods in Evolution (Supervisors: Prof. Dr. Alexander Mielke, Prof. Dr. Ulisse Stefanelli)


Together with Maciek Korzec from TU Berlin I organized a BMS Intensive Course on Evolution Equations and their Applications from November 27-29, 2013. For details see the website or the poster (PDF).


Self-heating in 2.54mm x 2.54mm OLED sample on glass substrate. The interplay between temperature activated hopping transport and Joule heating leads to complicated electrothermal feedback, leading to S-shaped current-voltage characteristics with rewgions of negative differential resistance. This behavior was studied in Matheon project SE2 in cooperation with the Dresden Integrated Center for Applied Physics and Photonic Materials (IAPP).

Hole density, hole current density and electrostatic potential in Vertical Organic Field-Effect Transistor for applied drain voltage and opening of gate. This behavior was studied in Matheon project SE18 in cooperation with the Dresden Integrated Center for Applied Physics and Photonic Materials (IAPP).