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.

"Student Compact Course on Variational Methods and Fluids" online (12th -- 23rd October 2020) and "Kick-off Conference" online (26th -- 30th October 2020) within the Thematic Einstein Semester, winter term 2020/21: A broad program of online lectures on gradient structures, Hamiltonian systems, GENERIC and port-Hamiltonian structures, evolutionary Gamma-convergence, large deviations theory, structure-preserving numerical methods, and much more was offered to about 100 participants of the ”Student Compact Course”. Interested PhD-students had the opportunity to give short presentations of their work and to further explore the TES topics. Subsequently, a ”Kick-off Conference” with 25 invited talks and about 150 participants took place.

On October 23rd 2019, the organisers of the Berliner Oberseminar "Nonlinear Partial Differential Equations" (Langenbach-Seminar) hosted a colloquium in honour of Prof. Dr. Herbert Gajewski's 80th birthday. Ansgar Jüngel (TU Vienna) gave a special lecture titled "Cross-diffusion systems: from spin semiconductors to biological populations with stochastic forcing", which touched on several of Herbert Gajewski's research fields. Prof. Dr. Herbert Gajewski held the offices of deputy director and acting director of the WIAS and was head of Research Group 1.

9th -- 13rd September 2019, PDE 2019: Partial Differential Equations in Fluids and Solids

Prof. Dr. Karen M. Gambaryan, head of the Semiconductor and Microelectronics Dept. at Yerevan State University, Armenia, has been visiting our institute for the months of July and August 2019. During his visit which was funded via an award by the German Academic Exchange Service (DAAD), Karen was introduced to the software library Sphinx and has performed systematic simulations of InAsSbP quantum dots that resemble the realistic systems obtained in his lab using liquid phase epitaxy (LPE).

Several members of RG1 and the Weierstrass Group participated in the "International Congress on Industrial and Applied Mathematics"(15th --19th July 2010, Valencia, Spain).

After Mr. Thomas Frenzel's PhD thesis defense (”On the derivation of effective gradient systems via EDP-convergence") on 26th June, 2019.

On 31st January and 1st February 2019, the kickoff meeting of the ECMI Special Interest Group "Modelling, Simulation and Optimization in Electrical Engineering" took place at WIAS; the meeting was organized by Nella Rotundo (RG1), Patricio Farrell (RG3) and Dirk Peschka (Weierstrass Group).

Within the framework of the workshop "Analysis of Evolutionary and Complex Systems", a colloquium in honor of Alexander Mielke's 60th birthday took place on 26th September 2018.

On occasion of his 80th birthday, Prof. Dr. Konrad Gröger was awarded a Honorary Medal by the Czech Mathematical Society for his longlife contribution to cooperation between Czech and German mathematicians, see photos below.

The junior prize of the International Society for the Interaction of Mechanics and Mathematics (ISIMM) 2018 was awarded to Matthias Liero. The recipient of the prize is to selected among the researchers who made significant contributions linking Mathematics and Mathematical Physics. Matthias Liero's research is focused on the mathematical analysis of partial differential equations, e.g. describing the electrothermal interplay in organic light-emitting diodes (OLEDs). He is already the second awardee of the ISIMM junior prize of our research group.