Michele Ruggeri (TU Wien) Vienna University of Technology
Magnetic phenomena have been known for millennia, since in ancient times people noticed that lodestones (magnetite) could attract iron. Nowadays, the use of magnetic materials in technological processes is ubiquitous (e.g., energy transformation and data storage). Moreover, they play an essential role in many devices (e.g., magnetic sensors and actuators, electric motors and generators, microphones, loudspeakers, telephones, and hard disk drives).
Magnetic processes are multiscale and multiphysics phenomena and their modeling involves nonlinear partial differential equations (PDEs), nonlocal effects, nonconvex energies and constraints.
In this lecture, we give an overview on the mathematics behind magnetic materials, touching on several topics, mostly in the fields of mathematical modeling, analysis, and numerics.

• Modeling: magnetic moment, type of magnetism, atomistic vs. continuum theories, micromagnetics, hysteresis, Maxwell equations, Landau-Lifshitz-Gilbert (LLG) equations.
• Analysis: micromagnetic energy minimization, thin-film limits, existence and (non)uniqueness results for LLG equations.
• Numerics: numerical treatment of Maxwell and LLG equations, finite element methods, boundary element methods, unconditional stability and convergence.

Further topics could be also addressed depending on students' interests.

Course Webpage

• Ulisse Stefanelli (Uni Wien)
• Luca Scarpa (Uni Wien)
• Gerald Teschl (Uni Wien)

University of Vienna
This is a topics course on nonlinear partial differential equations of evolution type. It is organized in three blocks:

• Evolution problems in metric spaces (U. Stefanelli, from March 4th to April 1st),
• Semilinear parabolic equations: deterministic and stochastic (L. Scarpa, from April 22nd to May 20th),
• Nonlinear Schrödinger equations (G. Teschl, from June 3rd to June 24th).

Course Webpage

Nikos Kavallaris (University of Chester)
Vienna University of Technology

Aim: Blow-up theory for nonlinear deterministic and stochastic partial differential equations.
Content:

• Introduction to the concept of blow-up
• Finite-time Blow-up: ODEs vs PDEs
• Main methods for proving the existence of finite-time blow-up for some key nonlinear PDEs
• Some techniques for proving finite-time blow-up for some stochastic partial differentials equations (SPDEs)

Poster

Marcel Braukhoff (TU Wien)
Sem.R. DA grün 03 C (TU Wien)
Elliptical equations occur in various applications in physics, chemistry and biology. Examples are equations from electrostatics and gravitation. Furthermore, elliptical equations can be found as stationary problems describing the diffusion of a chemical in a solution. If one wants to calculate the solutions numerically in these cases, it turns out that the numerical methods usually converge faster the more regular the solution of the elliptical equation is. On the one hand, direct methods using the fundamental solution are treated. On the other hand, the $H^m$ regularity and the Hölder regularity of solutions of elliptic equations are also proved.

Course Webpage

Esther Daus (TU Wien)
Sem.R. DA grün 03 C (TU Wien)
Many applications in physics, chemistry and biology can be modeled by reaction-(cross) diffusion systems, which describe the evolution of the densities or concentrations of a multicomponent system. The focus of the first part of the lecture will be on the mathematical properties of reversible reaction-diffusion systems based on entropy methods. Our goal will be to show how the entropy estimate can be used systematically to get bounds leading to the existence of strong or weak solutions, as well as bounds for the convergence rate to equilibrium.
The second part of this lecture will then be devoted to the study of the existence theory for cross-diffusion systems used in applications, for instance a population dynamics model describing the segregation of species due to competition or the Maxwell-Stefan equations modeling the evolution of a gaseous mixture.

Course Webpage

Luca Lussardi (Politecnico di Torino)
University of Vienna
The aim of the course is to give an overview of the main techniques for the Plateau problem, that is to find a surface with minimal area that spans a given boundary curve in $\mathbb{R}^3$. This problem dates back to the physical experiments of Joseph Plateau who tried to understand the possible configurations of soap films. From the mathematical point of view the problem is very hard and a lot of possible formulations are available: perhaps still today none of these answers is the answer to the original formulation by Plateau. In this course first of all I will briefly introduce the problem showing that, at least in the smooth case, if the first variation of the area vanishes then the surface must have zero mean curvature. Then I will describe how the classical solution by Douglas and Rado works, and I will pass to modern formulations of the problem in the context of geometric measure theory: finite perimeter sets approach, currents approach, and minimal sets approach. Possibly, some physical experiments with soap films could be done in order to clarify advantages and drawbacks of the approaches.

For more details about the course, please visit the relative

webpage

.

Francis Filbet (Université Toulouse III & Institut Universitaire de France)
ESI, Vienna (Boltzmanngasse 9, 1090 Vienna)
In this lectures we will focus on the Boltzmann equation for rarefied gas dynamics. After a short introduction of the physical background we will review some basic tools in analysis to study the existence of solution for the homogeneous Boltzmann equation. Then, some numerical approximation based on spectral methods will be presented and a rigorous convergence study will be performed.

Course Webpage

Jan Haskovec (King Abdullah University of Science and Technology, Thuwal, KSA)
TU Wien

• Systems of self-propelled particles, the Cucker-Smale model as a proptotypical example, asymptotic flocking.
• Attraction-repulsion-orientation model. Milling, double-milling and other patterns.
• Models with noise and delay.
• Mesoscopic and hydrodynamic descriptions and their well posedness.

Course Announcement

Gaurav Dhariwal (TU Wien)
TU Wien

• Probability and measure
• Lebesgue integration
• Random variables
• Discrete stochastic processes
• Brownian Motion
• Itô Lemma
• SDEs

Course Announcement

Xiuqing Chen (Beijing University of Posts & Telecommunications)
TU Wien

• Basic facts concerning weak convergence and weak compactness for functions and measures.
• Strong compactness in $L_p(0,T;B)$ spaces (i.e. Aubin-Lions-Dubinskii lemmas).
• Application to porous media/fast diffusion equations.
• Application to reaction-diffusion equations.

Course Announcement

Milan Pokorný (Charles University, Prague)
TU Wien
: On Wednesdays the lecture time has been rescheduled to .

Poster

Heiko Gimperlein (Heriot-Watt University)
TU Wien

• Modelling of interface problems between materials: interface conditions and friction laws
• Obstacle problems, friction and contact: (free) time-independent boundary problems as constrained on nonsmooth variational problems, solution using Uzawa and semismooth Newton methods
• Nonlinear analysis of variational inequalities: functional analytic background, classical theorem on wellposedness and abstract approximation, regularity of solutions
• Approximation by finite and boundary elements - from basics to current research: BEM for dummies, variational inequalities and penalty formulations, error analysis, adaptivity, advanced approximation methods, maybe coupling of FEM and BEM
• Towards time-dependent dynamic contact problems

Course Webpage

Nikos Katzourakis (University of Reading)
TU Wien

Part I General Theory

• History, Examples, Motivation and First Definitions
• Second Definitions and Basic Analytic Properties of the Notions
• Stability Properties of the Notions and Existence via Approximation
• Mollification of Viscosity Solutions and Semiconvexity
• Existence of Solution to the Dirichlet Problem via Perron's Method
• Comparison results and Uniqueness of Solution to the Dirichlet Problem

Part II Applications

• Minimisers of Convex Functionals and Viscosity Solutions of the Euler-Lagrange PDE
• Existence of Viscosity Solutions to the Dirichlet Problem for the Laplacian

Poster

and

TISS page

Michael Dreher (University of Konstanz)
TU Wien, Sem. R. DB gelb 03

• Thursday 10:00-13:00, TU Freihaus, Sem.R. DA grün 03 C
• Friday 14:00-17:00, TU Freihaus, Sem.R. DA grün 03 A

• Pseudodifferential operators and their mapping properties
• Elliptic operators in the full space and their inverses
• Boundary conditions and BVPs
• Applications to fluiddynamics (QHD)
• Hyperbolic problems and Fourier integral operators

Poster

and

lecture notes

Alan Lindsay (University of Notre Dame)
TU Wien, Sem. R. DB gelb 03

Poster

and detailed

abstract

Amit Einav (University of Cambridge, UK)
TU Wien, Sem. R. DB gelb 03
14:00-16:00

Poster

Mario Bukal (University of Zagreb)
TU Wien, SEM 101B

• Axiomatic foundation of entropies in information theory (Rényi and Tsallis entropies)
• Entropy power, concavity, and related functional inequalities
• Long-time behavior of nonlinear diffusion equations
• Markov decision processes
• Perception - action cycles and information-to-go

Course Announcement

Mariya Ptashnyk (University of Dundee, UK)
TU Wien

• methods of periodic homogenization
• multiscale modelling and analysis of transport and reaction processes in perforated and partially perforated domains
• duality-porosity
• locally-periodic homogenization
• multiscale analysis of equations of linear elasticity and viscoelasticity
• main ideas of $\Gamma$- and $G$-convergences

Course Announcement

Pina Milišić (University of Zagreb)
TU Wien

• Motivating examples
• Finite-dimensional optimal control problems
• Optimal control of elliptic PDEs
• Optimal control of semilinear elliptic PDEs

Course Announcement

Lehel Banjai (Heriot-Watt University)
TU Wien

• Introducing TDBIEs and their discretizations
• Convolution quadrature and a typical analysis of the time-discretization
• Implementation: Use of lower triangular Toeplitz matrices
• Advanced topics (unlikely to cover all): higher-order methods, FEM-BEM coupling, non-linearities

Course Announcement

and

TISS page

Florian Rupp (German University of Technology in Oman)
TU Wien

• Stochastic modeling of biological processes from first principles
• Ito's and Stratonovich's stochastic integrals
• Existence and uniqueness of solutions of stochastic ordinary differential equations (SODEs) in the strong and weak sense, boundedness of solutions of SODEs in the positive orthant, strong and weak Taylor schemas and the simulation of paths
• Fokker-Planck equation and the evolution of densities
• Random Dynamical Systems, Hopf-bifurcations in SODE-driven systems, crater densities and the approximation of strange attractors during stochastic Hopf-bifurcations.

Course Announcement

and

Schedule

Wilhelm Schlag (University of Chicago)
Faculty of Mathematics, University of Vienna, Seminar room 15, 3rd floor, OMP1
25.-27.09.2013, Wed, Thu, Fri 10:00 - 12:00
Aleksey Kostenko and Gerald Teschl
We will present some of the tools developed by Bourgain, Goldstein, and the speaker to study a class of Schrödinger operators on both the line Z as well as higher-dimensional lattices. These methods rely on properties of subharmonic functions, but also involve ideas from semi-algebraic sets.

Poster