Geometric partial differential equations: Theory, numerics and applications

This workshop concentrated on partial differential equations involving stationary and evolving surfaces in which geometric quantities play a major role. Mutual interest in this emerging field stimulated the interaction between analysis, numerical solution, and applications

Challenges in Optimization with Complex PDE-Systems (hybrid meeting)

The workshop concentrated on various aspects of optimization problems with systems of nonlinear partial differential equations (PDEs) or variational inequalities (VIs) as constraints. In particular, discussions around several keynote presentations in the areas of optimal control of nonlinear or non-smooth systems, optimization problems with functional and discrete or switching variables leading to mixed integer nonlinear PDE constrained optimization, shape and topology optimization, feedback control and stabilization, multi-criteria problems and multiple optimization problems with equilibrium constraints as well as versions of these problems under uncertainty or stochastic influences, and the respectively associated numerical analysis as well as design and analysis of solution algorithms were promoted. Moreover, aspects of optimal control of data-driven PDE constraints (e.g. related to machine learning) were addressed

Gradient flows as a selection procedure for equilibria of nonconvex energies

For atomistic material models, global minimization gives the wrong qualitative behavior; a theory of equilibrium solutions needs to be defined in different terms. In this paper, a concept based on gradient flow evolutions, to describe local minimization for simple atomistic models based on the Lennard–Jones potential, is presented. As an application of this technique, it is shown that an atomistic gradient flow evolution converges to a gradient flow of a continuum energy as the spacing between the atoms tends to zero. In addition, the convergence of the resulting equilibria is investigated in the case of elastic deformation and a simple damaged state

Abstracts of CSc. theses in mathematics

summary:Malý, Marek: Studentized $m$-estimators and their $k$-step. Tran, Quoc Viet: Some adaptive estimators in regression models. Petkevič, Vladimír: An extended dependency based specification of underlying representations of sentences. Plecháč, Petr: Numerical analysis of Takens-Bogdanov points. Brzezina, Miroslav: Bases, essential bases and Wiener's criterion in balayage spaces. Kastrová, Jela: 10-vertices coloured 3-configurations and some quasigroup identities. Kottas, Jiří: On the regularity of weak solutions to elliptic problems. Neumann, Jan: Contribution to the spectral theory of variational inequalities. Herbst, Tomáš: Estimation of lifetime characteristics from censored samples proportion hazards model. Majeed, Kauwd Khalf: The projective special linear group $PSL(6,2^a)$. Rokyta, Mirko: Euler equations and their numerical solution by the finite volume method. Laušmanová, Monika: Asymptotic methods in the theory of stochastic controlled systems. Krupková, Olga: Variational analysis on fibered manifolds over one-dimensional basis. Čechová, Markéta: Estimations of the parameters in the linear processes. Málek, Josef: Non-newtonian incompressible fluids without memory

International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more