Partial Differential Equations

Many fundamental processes in nature and technology can be described by partial differential equations. The research group is working on the analytical theory of such equations (existence, uniqueness, qualitative behaviour) and on the development and implementation of algorithms for their numerical solution. The algorithms are used for the numerical simulation in industrial applications. The functionality of modern materials, for instance, relies on the complex interplay of effects on several length and time scales as well as on different physical effects, such as mechanics, thermodynamics, optics, and electromagnetism. The main topics of research are mathematical models of carrier transport in semiconductors and optoelectronic devices and reaction-diffusion equations for the transport of dopants in solids. Furthermore, nonlinear material models for linearized and nonlinear elasticity and plasticity as well as for systems with internal variables are under study. In this context, we develop in particular methods for abstract evolutionary equations, e.g. gradient systems, and for multiscale problems.

We are honored to announce the release of ”Trotter--Kato Product Formulae”, the final work of our late esteemed colleague Hagen Neidhardt, co-authored with Valentin Zagrebnov and Takashi Ichinose. The book provides a comprehensive overview of operator-norm convergent Trotter--Kato Product Formulae on Hilbert and Banach spaces. It includes pioneering results on operator-norm convergent product formulas for solution operators of non-autonomous Cauchy problems, along with insights into unitary and Zeno product formulas.

Georg Heinze has been appointed as a member of the GAMM Juniors. Congratulations!

The international workshop “AMaSiS 2024: Applied Mathematics and Simulation for Semiconductor Devices" was organized by Annegret Glitzky, Matthias Liero, Michael O'Donovan (RG 1), Markus Kantner (RG 2), Patricio Farrell (LG 5), and Josef Weinbub (Silvaco Vienna) and held at the Humboldt University of Berlin and the Leibniz Headquarters from September 10 to 13, 2024. AMaSiS 2024 started with two tutorial sessions and had its focus on the mathematical modeling and numerical simulation of semiconductor devices. It dealt with quantum and semiclassical transport, electronic structure theory, computational materials science, and on upscaling from quantum mechanics and particle systems to continumm scale modes. With 19 invited talks, 19 contributions, and 57 participants from nine countries AMaSiS 2024 was a great success. It was part of the “Thematic Einstein Semester: Mathematics for Quantum Technologies", funding via the Einstein Foundation and the Berlin Mathematics Research Center MATH+ is gratefully acknowledged.

Alexander Mielke was awarded the the ISIMM Senior Prize 2024 by the International Society for the Interaction of Mechanics and Mathematics at the bi-annual "Symposium on Trends of Applications of Mathematics to Mechanics" on April 4, 2024. Congratulations!

The workshop Optimal Transport from Theory to Applications: Interfacing Dynamical Systems, Optimization, and Machine Learning was jointly organized by members of RG 1 (Matthias Liero), RG 6 (Pavel Dvurechensky), WG DOC (Jia-Jie Zhu), and TU Berlin (Gabriele Steidl) and held at the Humboldt University of Berlin from March 11 to 15, 2024 . The emphasis was on the interaction between optimal transport and statistics, machine learning, imaging, optimization, and dynamical systems. With 25 invited talks, 28 contributions, and over 100 participants, the event was a great success. Funding via DFG and MATH+ is gratefully acknowledged.

Georg Heinze successfully defended his PhD thesis entitled ”Graph-based nonlocal gradient systems and their local limits” on 15th March, 2024. Congratulations!