Workshop on Nonlinear Parabolic PDEs

May 20 - May 24, 2024

Nonlinear evolutionary partial differential equations are of fundamental importance in mathematical analysis. They are used to model time-dependent phenomena such as flows in porous media, turbulent filtration processes, groundwater flows through gravel or fractured crystalline rocks, shallow water waves, turbulent polytropic filtration of gas or the moving boundary between two phases of a material undergoing a phase change (for instance the melting of ice to water, Stefan problem. Such phenomena or processes are typically modeled by parabolic PDE’s with singular and/ or degenerate.

In recent years, there have been quite a number of breakthroughs in the theory of singular and degenerate parabolic PDEs. For example, it was shown that weak solutions of the porous medium equation are higher integrable in the sense of Elcrat and Meyers. This result was extended to porous medium type systems and Trudinger’s equation. Moreover, several parameter ranges of doubly nonlinear parabolic equations are nowadays covered. Also, the Hölder continuity of weak solutions is widely understood for both non-negative and signed solutions. There has also been significant progress in regularity theory for the Stefan problem. On the other hand, many important problems remain unresolved. Even the uniqueness of weak solutions to doubly non-linear equations is not yet fully understood.

The proposed workshop will focus on the following themes related to (doubly) nonlinear parabolic PDEs

  • comparison principles and uniqueness of weak solutions, 
  • boundary regularity, 
  • regularity of the spatial gradient and  
  • behavior of solutions in the subcritical range.

As will become apparent, the novelties are not mutually exclusive and several themes can overlap in a specific research problem.

Seminars Scroll to the next upcoming seminar

Participants

Name University Country Arrival and Departure
Sun-Sig
Byun
University: Seoul National University City: Korea Arrival and Departure: -
Fabian
Bäuerlein
University: Paris Lodron University of Salzburg City: Austria Arrival and Departure: -
Verena
Bögelein
University: Paris Lodron University of Salzburg City: Austria Arrival and Departure: -
Simone
Ciani
University: University of Bologna City: Italy Arrival and Departure: -
Frank
Duzaar
University: Paris Lodron University Salzburg City: Austria Arrival and Departure: -
Cristiana
De Filippis
University: University of Parma City: Italy Arrival and Departure: -
Julian
Fischer
University: Institute of Science and Technology Austria City: Austria Arrival and Departure: -
Ugo
Gianazza
University: Department of Mathematics "F. Casorati", University of Pavia City: Italy Arrival and Departure: -
Raffaella
Giova
University: University of Naples Parthenope City: Italy Arrival and Departure: -
Peter
Hästö
University: University of Helsinki City: Finland Arrival and Departure:   -  
Sunghan
Kim
University: Uppsala University City: Sweden Arrival and Departure: -
Wontae
Kim
University: Aalto university City: Finland Arrival and Departure: -
Juha
Kinnunen
University: Aalto University City: Finland Arrival and Departure: -
Naian
Liao
University: University of Salzburg City: Austria Arrival and Departure: -
Erik
Lindgren
University: Uppsala University City: Sweden Arrival and Departure: -
Paolo
Marcellini
University: University of Florence City: Italy Arrival and Departure: -
Kristian
Moring
University: University of Duisburg-Essen City: Germany Arrival and Departure: -
Kim
Myyryläinen
University: Aalto University City: Finland Arrival and Departure: -
Kaj
Nyström
University: Uppsala University City: Sweden Arrival and Departure: -
Jihoon
Ok
University: Sogang University City: Korea Arrival and Departure: -
Mikko
Parviainen
University: University of Jyväskylä City: Finland Arrival and Departure: -
Antonia
Passarelli di Napoli
University: Università degli Studi di Napoli "Federico II" City: Italy Arrival and Departure: -
Carlos
Perez Moreno
University: Ikerbasque City: Spain Arrival and Departure: -
Christoph
Scheven
University: University Duisburg-Essen City: Germany Arrival and Departure: -
Sebastian
Schwarzacher
University: Uppsala University City: Sweden Arrival and Departure: -
Leah
Schätzler
University: University of Salzburg City: Austria Arrival and Departure: -
Stefanie
Sonner
University: Radboud University City: Netherlands Arrival and Departure: -
Bianca
Stroffolini
University: University of Naples City: Italy Arrival and Departure: -
Ulisse
Stefanelli
University: University of Vienna City: Austria Arrival and Departure: -
Michael
Strunk
University: Paris-Lodron-Universität Salzburg City: Austria Arrival and Departure: -
Lauri
Särkio
University: Aalto University City: Finland Arrival and Departure: -
Shuntaro
Tsubouchi
University: University of Tokyo City: Japan Arrival and Departure: -
José Miguel
Urbano
University: KAUST and Universidade de Coimbra City: Saudi Arabia Arrival and Departure: -
Vincenzo
Vespri
University: University of Florence City: Italy Arrival and Departure: -
Matias
Vestberg
University: Uppsala University City: Sweden Arrival and Departure: -
Anna
Zatorska-Goldstein
University: University of Warsaw City: Poland Arrival and Departure: -