Forschungsseminar

Wintersemester 2018/19

  • 29. Oktober 2018: Gieri Simonett  (Nashville)
    On the motion of a rigid body with a cavity filled with a viscous liquid

    Abstract. In this talk, I will consider the motion of a rigid body with an interior cavity that is completely filled with a viscous fluid, in the absence of exterior forces. The equilibria of the system will be characterized and their stability properties are analyzed. It will be shown that equilibria associated with the largest moment of inertia are normally stable, while all other equilibria are normally hyperbolic. Leray-Hopf solution for this system becomes strong at some time and then persists as a strong L_2 -solution. Moreover, it also follows that the relative velocity goes to zero. Using recent work by the author, Prüss, Wilke, and Zacher, we present a rather short and direct proof that any of these solutions converges to an equilibrium at an exponential rate. This reflects the well-known stabilizing effect that the viscous fluid exerts on the motion of the rigid body. In addition, we will characterize the critical spaces for the governing evolution equation, and we will show how parabolic regularization in time-weighted spaces affords great flexibility in establishing regularity and stability properties for the system. Our approach is based on the theory of Lp-Lq maximal regularity. (Joint work with G. Mazzone and J. Prüss.)

  • 05. November 2018:  Franz Gmeineder  (Bonn)
    Regularity for  Quasiconvex Problems with Linear Growth from Below

    Abstract.  Quasiconvexity in the sense of Morrey is a fundamental notion in the vectorial calculus of variations. In fact, for a broad class of multiple integrals, it is a necessary and sufficient condition for sequential weak lower semicontinuity and hence the gateway to the existence of minima. The other instrumental ingredient is coerciveness, in turn being implied by a strong version of quasiconvexity. In this talk we report on recent work on the partial regularity of minima of strongly quasiconvex (p,q)-growth type functionals – i.e., having p-power growth from below and q-power growth from above – for the almost optimal range of p and q. By the work of Bouchitt ́e, Fonseca and Maly ́, this range is essentially determined by the availability of a measure representation for the relaxed functionals. Also, p is allowed to be 1 in this setting. This talk is based on joint work with J. Kristensen (Oxford).

  • 19. November 2019:  Simon Markfelder  (Würzburg)
    On non- / uniqueness of solutions to the compressible Euler equations

    Abstract:  We summarize some results concerning non- / uniqueness of solutions to the compressible Euler equations in multiple space dimensions. These equations describe the time evolution of a compressible inviscid fluid. We focus on a special type of initial data, namely those which are constant in each of the two half spaces (Riemann data). One can find one solution to such an initial value problem by solving a corresponding one dimensional Riemann problem. However for many choices of the two initial states there are infinitely many other solutions, what is shown by convex integration.

  • 26. November 2018:  Marius Müller  (Ulm)
    On Gradient Flows with Obstacles and Euler's Elastica

    Abstract:  In this talk, we examine steepest energy descent flows subject to obstacle constraints. We consider higher order frameworks, where the maximum principle does not apply. The constructed flows can be understood as gradient flows in the sense of Ambrosio, Gigli and Savare. To ensure existence of such flows, one often imposes continuity conditions on the metric slope of the energy, which turn out to be restrictive for nonlinear obstacle problems.

    One can circumvent these conditions given a suitable compactness of the discrete trajectories in the De Giorgi Minimizing Movement Scheme. The required compactness is easy to obtain for a large class of fourth order equations with Navier boundary conditions. An important application of this is the 1-dimensional Willmore flow with obstacle constraint, for which we will study long-time-behavior, finding asymptotic properties that match up with the results of A. Dall'Acqua and K. Deckelnick on the time-independent variational problem.

  • 03. Dezember 2019:  Lisa Beck (Augsburg)
    On the minimization of convex, variational integrals of linear growth

    Abstract.  We study the minimization of functionals of the form \int_\Omega f(Du)dx with a convex integrand f of linear growth, among all functions in the Sobolev space W1,1 with prescribed boundary values. Due to insufficient compactness properties of these Dirichlet classes, the existence of solutions does not follow in a standard way by the direct method in the calculus of variations and might in fact fail, as it is well-known already for the non-parametric minimal surface problem. In such cases, the functional is extended suitably to the space of functions of bounded variation via relaxation, and for the relaxed functional one can in turn guarantee the existence of minimizers. However, in contrast to the original minimization problem, these so-called generalized minimizer might in principle have interior jump discontinuities or might not attain the prescribed boundary values. After a short introduction to the problem I want to discuss what is known about the regularity of generalized minimizers. In particular, I will review several results which were obtained in the last years in cooperation with Miroslav Bulíček (Prague), Franz Gmeineder (Bonn), Erika Maringová (Prague), and Thomas Schmidt (Hamburg).

  • 17. Dezember 2018:  Dirk Blömker (Augsburg)
    Stochastic Motion of Droplets in the Cahn-Hilliard Equation

    Abstract.  We study the stochastic Cahn-Hilliard equation, which is a model describing the phase separation and subsequent coarsening of binary alloys. In the nucleation regime almost spherical droplets appear, and we approximate the infinite dimensional stochastic dynamics of these droplets by the motion along a finite dimensional deterministic slow manifold. The main results are effective equations (given by stochastic ordinary differential equations) on the slow manifold and the stochastic stability of the manifold.

  • 21. Januar 2019: Christina Lienstromberg (Bonn)
    Non-Newtonian Thin Film Equations

    Abstract.  We study the existence of solutions to a degenerate parabolic non-Newtonian thin-film equation with shear-thinning rheology. Originating from the Navier–Stokes system the equation under consideration may be derived by lubrication theory and under the assumption that capillarity is the only driving force. The fluid’s shear-shinning rheology is described by the so-called Ellis constitutive law. It is shown that the problem is locally well-posed in the classical sense for flow behaviour exponents α ≥ 2. Given positive initial data, classical solutions stay positive as long as they exist as classical solutions. Moreover, the existence of non-negative global weak solutions is established for non-negative initial data and all flow behaviour exponents
    α ≥ 2.

  • 30. Januar 2019: Lauri Viitasaari (Aalto University, Finland)
    Pathwise Stieltjes integrals of discontinuously evaluated stochastic processes

    Abstract.  In this talk we study the existence of pathwise Stieltjes integrals for Hölder continuous integrator and integrand having infinite p-variation for all values of p, and we discuss a notion of sufficient variability for the integrand which ensures the existence of the integral in a pathwise sense. We also show that the integral can be defined as a limit of Riemann-Stieltjes sums for a large class of processes, and provide new estimates on the accuracy of numerical approximations of such integrals.

    and as well

  • 30. Januar 2019: Michael Hinz (Bielefeld)
    Semilinear PDE on fractals

    Abstract. We first give a short introduction to analysis on fractal state spaces and the typical difficulties involved. We then discuss gradient operators and certain semilinear PDEs and briefly explain two recent results. The first is a metric graph approximation for a Burgers type equation, the second is a law of large numbers for an exclusion process on a fractal.


Sommersemester 2018

  • 18. Juni 2018: Julian Scheuer (Freiburg/Ulm)
    Harnack inequalities for evolving hypersurfaces

  • 28. Mai 2018: Florian Behr (Gießen)
    Periodische Lösungen der Gross-Pitaevskii-Gleichungen in der Kreisscheibe

  • 14. Mai 2018: Jukka Kemppainen (Oulu)
    Long-time behaviour of non-local in time Fokker-Planck equations via the entropy method

  • 12.-13. April 2018: Evolutionsgleichungen in Ulm 2018
    Workshop zur Seniorprofessur von Wolfgang Arendt

  • 9. April 2018: Daniel Hauer (Sydney)
    Fractional powers of monotone operators in Hilbert spaces

Wintersemester 2017/2018

  • 12. Februar 2018: Tatsuya Miura (Max-Planck-Institut Leipzig)
    Least energy elastic curves with boundary conditions

  • 31. Januar 2018: Sita Siewert (Tübingen/Ulm)
    Dynamische Bündel und Moduln

  • 15. Januar 2018: Athanasios Stylianou (Kassel)
    Modelling pattern formation on the surface of a ferrofluid

  • 6. November 2017: Jochen Glück (Ulm)
    Ein neuer Zugang zu Operatordilatationen

  • 4. Oktober 2017: Daniel Hauer (Sydney)
    Regularization effects of nonlinear semigroups

Sommersemester 2017

  • 25. Juli 2017: TULKKA in Ulm 
    Programm der TULKKA Tagung

  • 8. Juni 2017: Henrik Kreidler (Tübingen/Ulm)
    Das Primitivspektrum dynamischer Systeme

  • 22. Mai 2017: Nguyen Thieu Huy (Hanoi)
    Boundedness, periodicity and polynomial stability of solutions to evolution equations

  • 15. Mai 2017: Stephan Fackler (Ulm)
    Ein neuer Zugang zum Dilatationsresultat von Akcoglu–Sucheston

  • 19. April 2017: Tom ter Elst (Auckland)
    Analysis of the heat kernel of the Dirichlet-to-Neumann operator

Archiv Forschungsseminar

Wintersemester 2016/2017

  • 1. Februar 2017: Markus Kunze (Universität Konstanz)
    Von mikroskopischen zu makroskopischen Modellen in der mathematischen Biologie

  • 15.–18. Dezember 2016: AGFA+IAA Workshop in Blaubeuren
    Zahlreiche Vorträge im Rahmen des Workshops anlässlich der Schließung des Heinrich-Fabri Instituts. Programm zum Download

  • 12. Dezember 2016: Wolfgang Arendt (Ulm)
    Gebrochene Potenzen als Lösung eines Dirichlet-zu-Neumann Problems

  • 2. Dezember 2016 (Kolloqium): Jürgen Voigt (TU Dresden)
    Diffusion mit Absorption und ein maßtheoretisches Problem

  • 9. November 2016: Marcel Kreuter (Ulm)
    Die Perronlösung für das vektorwertige Dirichletproblem

Sommersemester 2016

  • 6. Juni 2016: Delio Mugnolo (FernUniversität in Hagen)
    Quantengraphen, spektrale Abschätzungen und Anwendungen

  • 1. Juni 2016: Tom ter Elst (Auckland)
    Hölder estimates for second-order operators on domains with rough boundary

  • 23. Mai 2016: Nick Lindemulder (TU Delft)
    Maximal Regularity with Weights for Parabolic Problems with Inhomogeneous Boundary Conditions

  • 29. April 2016 (Kolloquium): Tom ter Elst (Auckland)
    Does diffusion determine the drum?

  • 18. April 2016: Vincent Laurent (Ecole des Mines de Nancy)
    An alternative proof for the Faber–Krahn inequality

  • 11. April 2016: Jochen Glück (Ulm)
    Convergence of positive semigroups of kernel operators

  • 10. März 2016: Juhana Siljander (University of Jyväskyla) 
    Gradient estimates for the porous medium equation

Wintersemester 2015/2016

  • 8. Februar 2016: Manuel Bernhard (Ulm)
    Funktionalkalküle für Generatoren von Gruppen

  • 25. Januar 2016: Rico Zacher (Ulm)
    Li-Yau-Ungleichungen
     
  • 18. Januar 2016: Patryk Wolejko-Wolejszo (Ulm)
    Schwache Lösungen von nichtlinearen Integro-Differentialgleichungen im Hilbertraum

  • 7. Dezember 2015: Marcel Kreuter (Ulm) 
    Schwache Ableitung von Normen

  • 23. November 2015:
    Dominik Dier (Ulm)
    Maximale Regularität für nichtautonome Formen

    Stephan Fackler (Ulm)
    Banachskalen und nicht-autonome maximale Regularität auf Banachräumen

  • 20. November 2015 (Kolloquium): Jan Prüß (Martin-Luther-Universität Halle-Wittenberg) 
    Modeling and Analysis of Nematic Liquid Crystal Flows

  • 16. November 2015: Manfred Sauter (Ulm)
    Geometrische Kriterien für die Eindeutigkeit der approximativen Spur

  • 2. November 2015: Stefan Kunkel (Ulm)
    Nicht-lokale Neumannrandbedingungen

  • 26. Oktober 2016: Jochen Glück (Ulm)
    Spektrum und Asymptotik von Kontraktionshalbgruppen

  • 8. Oktober 2015: Mahamadi Warma (Puerto Rico)
    What are the three classical boundary conditions associated with the fractional Laplace?

Sommersemester 2015

  • 26. Juni 2015 (Kolloquium): 
    Gisele Goldstein (Memphis)
    The Ubiquitous Presence of Dynamic Boundary Conditions in Science

    Jerome Goldstein (Memphis)
    On the nature of the instability of radial power equilibira of a semilinear parabolic equation

  • 10. Juli 2015 (Kolloquium): Moritz Kassmann
    Scaling properties of integrodifferential operators

  • 16. Juli 2015: Moritz Gerlach (Saarbrücken)
    Ein Schätzer für das Spektrum des Laplace-Beltrami Operators

  • 17. Juli 2015:
    TULKKA Tagung in Ulm (Programm)

  • 14. August 2015: Lahcen Maniar (Marrakesch)
    Parabolic equations with dynamic boundary conditions of reactive­-diffusive type: well-posedness and null controllability

Wintersemester 2014/2015

  • 18. September 2014: Juhana Siljander (Helsinki)
    PDEs on metric measure spaces: regularity for the parabolic De Giorgi class

  • 28. Oktober 2014: Marie-Luise Hein (Ulm)
    Das Hartman-Grobman-Theorem für Semilineare Evolutionsgleichungen

  • 21. November 2014: Daniel Daners (Sydney)
    Uniform convergence of solutions to elliptic equations on domains with shrinking holes

Sommersemester 2014

Das Forschungsseminar findet im Sommersemester dienstags um 16:00 Uhr (s.t.) im Seminarraum 220 der Helmholtzstr. 18 statt.

  • 13. Mai 2014: Joachim Kerner (Stuttgart)
    Interacting many-particle systems and Bose-Einstein condensation on general compact quantum graphs

  • 20. Mai 2014: Matthias Keller (Jena)
    Analysis und geometry on graphs

  • 27. Mai 2014: Tom ter Elst (Auckland)
    The Dirichlet-to-Neumann operator via hidden compactness

  • 3. Juni 2014: Manuel Bernhard (Ulm)
    Das Langzeitverhalten eines einfachen Populationsmodells auf Lipschitz-Gebieten mit lokalem und konkavem Wachstum

  • 4. Juni 2014: Bastian von Harrach (Stuttgart)
    Inverse coefficient problems and shape reconstruction
    Seminarraum in der Helmholtzstr. 14

  • 10. Juni 2014: Luciano Abadias Ullod (Saragossa)
    Extensions of solutions of vector-valued fractional differential equations

  • 28. Juli 2014: Markus Haase (Delft)
    Systeme mit diskretem Spektrum und Wirkungen kompakter Gruppen

Archiv füherer Jahre

2014

  • 13.02.2014: Stephan Kunkel
    Eigenschaften von $C_0$-Halbgruppen auf $C(\overline{\Omega})$ mit nicht-lokalen Dirichlet-Randbedingungen

  • 13.02.2014: Włodzimierz Fechner (Katowice)
    On concave supra-multiplicative operators

  • 30.01.2014: Markus Kunze
    Gauß'sche Sobolevräume auf Gebieten

  • 06.02.2014: Khalid Akhlil

  • 09.01.2014: Manfred Sauter
    Über Sobolevfunktionen mit approximativer Spur $0$

2013

  • 12.12.2013: Jochen Glück
    Schließliche Positivität von Operator-Halbgruppen

  • 05.12.2013: Stephan Fackler
    Dilatationen und Funktionalkalkül auf L^p- & UMD-Räumen

  • 21.11.2013: Dominik Dier (Ulm)
    Maximale Regularität für nichtautonome Evolutionsgleichungen

  • 07.11.2013: Bobo Hua (MPI Leipzig)
    The Laplacians on graphs

  • 08.05.2013: Peter Sepitka
    Principal solutions of nonoscillatory self-adjoint linear differential systems

2012

  • 11.12.2012: Daniel Hauer (Ulm)
    Evolutionsprobleme für den p-Laplace Operator: asymptotisches Verhalten und Nichtexistenz

  • 22.11.2012: Włodzimierz Fechner (University of Silesia)
    Factorization theorems of Arendt type for additive monotone mappings

  • 20.11.2012: Tom ter Elst (University of Auckland)
    Diffusion determines the compact manifold

  • 06.11.2012: Vu Hoang (KIT Karlsruhe)
    Absolute continuity for partially periodic operators

  • 23.10.2012: Jochen Glück (Ulm)
    Strikt linear geordnete Halbgruppen und Einbettungen in die reellen Zahlen

  • 26.07.2012: El Maati Ouhabaz (Bordeaux)
    Observability, spectral theory and square functions
    und Daniel Hauer (Ulm)
    Ein Nichtexistenzsatz

  • 19.07.2012: Daniel Daners (Sydney)
    Krahn’s proof of the Rayleigh conjecture revisited

  • 05.07.2012: Abdelaziz Rhandi (Salerno)
    Schrödinger Operatoren mit polynomial wachsenden Diffusionskoeffizienten
    und Daniel Hauer (Ulm)
    On Hardy’s inequality with application to non-existence of global solutions

  • 28.06.2012: Delio Mugnolo (Ulm)
    Der diskrete p-Laplace-Operator

  • 31.05.2012: Moritz Gerlach (Ulm)
    Mittelergodensätze auf normierenden dualen Paaren

  • 24.05.2012: Karsten Urban (Ulm)
    Error estimates for Reduced Basis approximation of parabolic PDEs

  • 03.05.2012: Tobias Nau (Ulm)
    The Lp-Helmholtz projection in rectangular domain

  • 19.04.2012: James Kennedy (Ulm)
    Isoperimetric Inequalities for the Robin Laplacian

  • 13.02.2012: René Pröpper
    Wärmekernabschätzungen für metrische Graphen

  • 06.02.2012: Włodzimierz Fechner (Katowice)
    Functional inequalities motivated by the Lax-Milgram Theorem
    und Stefan Kunkel (München)
    Die Fokker-Planck-Gleichung

  • 30.01.2012: Omar El-Mennaoui (Agadir)
    Integralprodukt und Maximale Regularität

  • 23.01.2012: Jean-François Rault (Mainz)
    Nonlinear Convection in Reaction-Diffusion Equations under Dynamical Boundary Conditions

  • 16.01.2012: Lixin Cheng (Xiamen)
    On nonlinear epsilon-isometries on Banach spaces
    und Amru Hussein (Mainz)
    Maximal-accretive Laplacians on metric graphs

2011

19.12.2011

Existenz von Lösungen von degenerierten parabolischen PD-Gleichungen
Michal Chovanec (Ulm)

28.11.2011

Lp-maximal regularity for non-autonomous evolution equations and pi-integrability
Hafida Laasri (Ulm)

21.11.2011

Der Spektralsatz aus der Sicht der Quantenphysik
Dominik Müller (Stuttgart)

14.11.2011

Über die Wärmeleitungsgleichung mit nichtlokalen Bedingungen.
Jun.-Prof. Delio Mugnolo (Ulm)

08.11.2011 (Dienstag)

Divergenz-Form Operatoren in tent spaces
Sylvie Monniaux (Marseille)

24.10.2011

More regularity of solutions of subgradient systems
Daniel Hauer (Ulm)

27.07.2011

Randpaare und -tripel für quadratische Formen
Olaf Post

11.07.2011

Some miscellaneous results on generalised forms
Jun.-Prof. Delio Mugnolo

29.06.2011

Evolutionsfamilien für nichtautonome Differenzengleichungen
Fatih Bayazit

27.06.2011

Dimension reduction for a class of self-adjoint extensions with applications to graph-like systems
Prof. Konstantin Pankrashkin

20.06.2011

Non-autonomous Lp-maximal regularity
Hafida Laasri

06.06.2011

Spektrum und Asymptotik positiver Halbgruppen von Harris-Operatoren
Moritz Gerlach

30.05.2011

Ein Funktionalkalkül und dessen Konsequenz für Kosinus Funktionen
Domonik Dier

02.05.2011

An extension of Sobolev gradients to a quasi-Newton method
Parimah Kazemi

31.01.2011

B-konvexe Räume sind K-konvex
Stephan Fackler

24.01.2011

Fluss-invariante Mengen
Karl Ulrich

2010

20.12.2010

Der Satz von Doob
Moritz Gerlach

13.12.2010

Isometrien zwischen Sobolevräumen
Dr. Robin Nittka

06.12.2010

Asymptotic factorization of solutions of second order linear differential equations; from Liouville/Green to modern times.
Prof. Dr. Donald A. Lutz, San Diego State University

29.11.2010

Convergence of elliptic operators acting on varying Hilbert spaces
Jun.-Prof. Dr. Delio Mugnolo

22.11.2010

From Forms to Semigroups
Prof. Dr. Wolfgang Arendt

18.10.2010

Time-dependent quantum billiards
Dr. Zarif Sobirov, National University of Uzbekistan, Tashkent

20.09.2010

Martingalprobleme auf Banachräumen
Dr. Markus Kunze

19.07.2010

Fuchsian systems and middle convolution
Galina Filipuk
(Gast von W. Balser)

21.06.2010

Maximal Regularity of cylindrical parameter elliptic boundary value problems.
Tobias Nau

21.06.2010

Graph-like models for networks of thin tubes
Claudio Cacciapuoti

17.05.2010

Asymptotik positiver Halbgruppen
Moritz Gerlach

26.04.2010

Gleichungen mit Robin-Randbedingungen auf Lipschitzgebieten
Robin Nittka

01.02.2010

Perturbations of generators of C_0-semigroups and resolvent decay
Dr. Sebastian Kroll
Im E60 um 16 Uhr c.t

2009

19.10.2009

On the uniform convergence of double sine intergrals over R^2_+
Prof. Dr. Ferenc Moricz
Im E60 um 16 Uhr c.t

12.10.2009

Die Bedeutung des Dirichletschen Prinzips für die Algebraisierung kompakter Riemannscher Flächen
Arthur Gerber
Im E60 um 16 Uhr c.t

20.07.2009

H^{infinity}-calculus for L^p-realizations of truly cylindrical parameterelliptic boundary value problems using Kalton-Weis.
Tobias Nau
Im E60 um 16 Uhr c.t

13.07.2009

HARDY SPACES IN REINHARDT DOMAINS, AND HAUSDORF OPERATORS
Prof. Dr. Lev Aizenberg
Im E60 um 16 Uhr c.t

22.06.2009

Sobolev gradients and minimization in PDEs
Dr. Parimah Kazemi
Im E60 um 16 Uhr c.t.

15.06.2009

Hölder Continuity of Solutions of Elliptic Boundary Value Problems
Robin Nittka
Im E60 um 16 Uhr c.t.

25.05.2009

Self-Similarity for Flows
Prof. Dr. Krzysztof Frączek
Im E60 um 16 Uhr c.t.

18.05.2009

Existence of Solutions to certain non-linear Differential Equations with generalized Robin boundary conditions.
Dr. Markus Biegert
Im E60 um 16 Uhr c.t.

04.05.2009

Vector-valued diffusion with Wentzell-Robin coupled boundary conditions
Juniorprofessor Dr. Delio Mugnolo
Im E60 um 16 Uhr c.t.

27.04.2009

Reduction problems in the general case
Dr. Kana Ando
Im E60 um 16 Uhr c.t.

2008

15.12.2008

Über ein Resultat von H. Vogt zur Bestimmung des regulären Teils einer positiven symmetrischen Form
Manfred Sauter
Universität Ulm
Im E60 um 16 Uhr c.t.

08.12.2008

Gaussian Estimates for degenerate parabolic problems
Michal Chovanec
Universität Ulm
Im E60 um 16 Uhr c.t.

01.12.2008

Quasi-linear elliptic equations with generalized Robin boundary conditions on bad domains
Dr. Markus Biegert, Unversität Ulm
Im E60 um 16 Uhr c.t.

27.11.2008

Über die Zulässigkeit von Beobachtungsoperatoren auf Banachräumen
Professor Dr. Omar El-Mennaoui
Université Ibnon Zohr, Agadir, Morocco
Im E60 um 14 Uhr c.t.

17.11.2008

Accurate and fast polynomial evaluation
Dr. Iwona Wrobel
Im E60 um 16 Uhr c.t.

10.11.2008

Sektorielle Formen und degenerierte sektorielle Diffenrenzialoperatoren
Prof. Dr. Wolfgang Arendt
Im E60 um 16 Uhr c.t.

03.11.2008

Linear monodromy of the Painleve and q-Painleve functions
Prof. Dr. Yousuke Ohyama
Osaka University (z.Zt. Strasbourg)
Im E60 um 16 Uhr c.t.