@misc{31951, author = {{Häsel-Weide, Uta and Nührenbörger, M. and Reinold, M.}}, isbn = {{978-3122009939}}, pages = {{80}}, publisher = {{Klett}}, title = {{{Das Zahlenbuch 3. Förderheft.}}}, year = {{2018}}, } @article{34664, author = {{Black, Tobias}}, issn = {{0036-1410}}, journal = {{SIAM Journal on Mathematical Analysis}}, keywords = {{Applied Mathematics, Computational Mathematics, Analysis}}, number = {{4}}, pages = {{4087--4116}}, publisher = {{Society for Industrial & Applied Mathematics (SIAM)}}, title = {{{Global Very Weak Solutions to a Chemotaxis-Fluid System with Nonlinear Diffusion}}}, doi = {{10.1137/17m1159488}}, volume = {{50}}, year = {{2018}}, } @article{34666, author = {{Black, Tobias}}, issn = {{0022-0396}}, journal = {{Journal of Differential Equations}}, keywords = {{Analysis, Applied Mathematics}}, number = {{5}}, pages = {{2296--2339}}, publisher = {{Elsevier BV}}, title = {{{Eventual smoothness of generalized solutions to a singular chemotaxis-Stokes system in 2D}}}, doi = {{10.1016/j.jde.2018.04.035}}, volume = {{265}}, year = {{2018}}, } @article{34667, author = {{Black, Tobias}}, issn = {{0362-546X}}, journal = {{Nonlinear Analysis}}, keywords = {{Applied Mathematics, Analysis}}, pages = {{129--153}}, publisher = {{Elsevier BV}}, title = {{{Global solvability of chemotaxis–fluid systems with nonlinear diffusion and matrix-valued sensitivities in three dimensions}}}, doi = {{10.1016/j.na.2018.10.003}}, volume = {{180}}, year = {{2018}}, } @article{8753, abstract = {{In a wide range of applications it is desirable to optimally control a dynamical system with respect to concurrent, potentially competing goals. This gives rise to a multiobjective optimal control problem where, instead of computing a single optimal solution, the set of optimal compromises, the so-called Pareto set, has to be approximated. When the problem under consideration is described by a partial differential equation (PDE), as is the case for fluid flow, the computational cost rapidly increases and makes its direct treatment infeasible. Reduced order modeling is a very popular method to reduce the computational cost, in particular in a multi query context such as uncertainty quantification, parameter estimation or optimization. In this article, we show how to combine reduced order modeling and multiobjective optimal control techniques in order to efficiently solve multiobjective optimal control problems constrained by PDEs. We consider a global, derivative free optimization method as well as a local, gradient-based approach for which the optimality system is derived in two different ways. The methods are compared with regard to the solution quality as well as the computational effort and they are illustrated using the example of the flow around a cylinder and a backward-facing-step channel flow.}}, author = {{Peitz, Sebastian and Ober-Blöbaum, Sina and Dellnitz, Michael}}, issn = {{0167-8019}}, journal = {{Acta Applicandae Mathematicae}}, number = {{1}}, pages = {{171–199}}, title = {{{Multiobjective Optimal Control Methods for the Navier-Stokes Equations Using Reduced Order Modeling}}}, doi = {{10.1007/s10440-018-0209-7}}, volume = {{161}}, year = {{2018}}, } @inproceedings{29425, author = {{Jiménez, F. and Ober-Blöbaum, Sina}}, booktitle = {{6th European Conference on Computational Mechanics}}, title = {{{Necessary optimality conditions for optimally controlled dissipative mechanical systems modelled through fractional derivatives}}}, year = {{2018}}, } @inproceedings{29427, author = {{Jiménez, F. and Ober-Blöbaum, Sina}}, booktitle = {{6th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2018}}, pages = {{50--55}}, title = {{{A fractional variational approach for modelling dissipative mechanical systems continuous and discrete settings}}}, volume = {{51(3)}}, year = {{2018}}, } @inproceedings{31371, author = {{Hoffmann, Max}}, booktitle = {{Beiträge zum Mathematikunterricht 2018}}, pages = {{815--818}}, publisher = {{WTM-Verlag}}, title = {{{Schnittstellenaufgaben im Praxiseinsatz: Aufgabenbeispiel zur „Bleistiftstetigkeit“ und allgemeine Überlegungen zu möglichen Problemen beim Einsatz solcher Aufgaben}}}, doi = {{10.17877/DE290R-19412}}, year = {{2018}}, } @article{31375, author = {{Grieser, Daniel and Hoffmann, Max and Koepf, Wolfram and Kramer, Jürg}}, journal = {{Der Mathematikunterricht}}, pages = {{48–54}}, title = {{{Anfängervorlesungen}}}, volume = {{64 (5)}}, year = {{2018}}, } @misc{31382, author = {{Hoffmann, Max}}, booktitle = {{Mathematische Semesterberichte}}, pages = {{299–301}}, title = {{{Rezension: Dörte Haftendorn: Kurven erkunden und verstehen – Mit GeoGebra und anderen Werkzeugen}}}, doi = {{10.1007/s00591-018-0222-y}}, volume = {{65}}, year = {{2018}}, } @book{31380, editor = {{Greefrath, Gilbert and Hoffmann, Max and Koepf, Wolfram}}, title = {{{Der Mathematikunterricht 64 (5): Mathematik in Schule und Hochschule – wie groß ist die Lücke und wie gehen wir mit ihr um?}}}, year = {{2018}}, } @article{33335, abstract = {{For a class of one-dimensional autoregressive sequences (Xn), we consider the tail behaviour of the stopping time T0=min{n≥1:Xn≤0}. We discuss existing general analytical approaches to this and related problems and propose a new one, which is based on a renewal-type decomposition for the moment generating function of T0 and on the analytical Fredholm alternative. Using this method, we show that Px(T0=n)∼V(x)Rn0 for some 0