【Seminar】The Dirichlet problem and boundary regularity for nonlinear parabolic equations | Prof. Professor Anders Björn, Linköping University and OIST TSVP Visiting Scholar

Speaker:  Professor Anders Björn, Linkoping University and OIST TSVP Visiting Scholar

Title: The Dirichlet problem and boundary regularity for nonlinear parabolic equations    

Abstract: The p-parabolic equation \[ \partial_t u = \Delta_p u := \dvg(|\nabla u|^{p-2}\nabla u) \] is a nonlinear cousin of the classical heat equation. As such, it offers both difficulties and advantages compared with the heat equation. In the talk, we consider the Perron method for solving the Dirichlet problem for the p-parabolic equation in general bounded domains in $R^{n+1}$. Compared to space-time cylinders, such domains allow the space domain to change in time. Of particular interest will be boundary regularity for such domains, i.e. whether solutions attain their boundary data in a continuous way. Relations between regular boundary points and barriers will be discussed, as well as some peculiar examples and surprising phenomena related to boundary regularity. Towards the end I will discuss the same type of questions for two other nonlinear cousins of the heat equation, the porous medium equation \[ \partial_t u = \dvg(u^m) \] and the so-called normalized p-parabolic equation \[ \partial_t u = |\nabla u|^{2-p}\Delta_p u. \] The talk is based on collaborations with Jana Bj\"orn (Link\"oping), Ugo Gianazza (Pavia), Mikko Parviainen (Jyv\"askyl\"a) and Juhana Siljander (Jyv\"askyl\"a).

TSVP Talk: "What Can Quantum Field Theory Teach Us About Black Holes (And Vice Versa)?" by Nick Dorey

TSVP Talk
Language: English (no interpretation). Target audience: General audience / everyone at OIST and beyond. Freely accessible to all OIST members and guests without registration (also via Zoom).

Graduate School Mini Course Series: Introduction to Supersymmetric QFT

Mini Course: Introduction to Supersymmetric QFT

[Series Starting Thursday April 18, 2024]

TSVP Talk: "Spectra of Complex Networks" by Izaak Neri

TSVP Talk
Language: English (no interpretation). Target audience: General audience / everyone at OIST and beyond. Freely accessible to all OIST members and guests without registration (also via Zoom).

[Seminar] Flows and Topological Changes During Tissue Morphogenesis

Speaker: Professor Luiza Angheluta-Bauer, Condensed Matter Physics, University of Oslo

Hosted by Professor Mahesh Bandi Nonlinear and Non-equilibrium Physics Unit

Abstract:

Collective structural arrangements and cell migration are important physical processes underlying tissue development and regeneration. Understanding the complexity of cell-cell interactions and the emergence of collective behaviors at the tissue scale presents formidable challenges both experimentally and theoretically.

In this talk, I will discuss recent theoretical work on the dynamical patterns that emerge at the tissue scale from localized rearrangements and topological defects. Using a multi-phase field model, we demonstrate that tissue fluidity stems from cell neighbor exchanges, serving as transient sources of vortical flow. This flow emerges from the relative dispersion of cells at a rate proportional to the frequency of rearrangements. Balancing collective migration with relative cell motion appears to be essential for maintaining tissue shape and fluidity. Using a cell-based model, we study the tissue's response to the presence of a vortex. While solid-like behavior tends toward conical shapes, localized fluidization triggers the transition to a tube, which is fundamental in biological tissues.

"Unraveling global change impacts to biodiversity and ecosystem services with interdisciplinary approaches" by Laura Dee (TSVP Seminar)

Seminar, as part of Thematic Program on Response Diversity
Language: English (no interpretation). Target audience: Students and Researchers from related fields.
Freely accessible to all OIST members and guests without registration (also via Zoom).

TSVP Workshop: The Future of Response Diversity and Ecosystem Stability

linked to TSVP Thematic Program:
Response Diversity and Ecosystem Stability (TP23RD)

"How can we measure the diversity of ecological interactions in the real world?" by Fredric Windsor (TSVP Seminar)

Seminar, as part of Thematic Program on Response Diversity
Language: English (no interpretation). Target audience: Students and Researchers from related fields.
Freely accessible to all OIST members and guests without registration (also via Zoom).

Panel Discussion: Publishing Science in a Rapidly Changing Publishing Landscape (with TSVP visitors)

Seminar, as part of Thematic Program on Response Diversity
Language: English (no interpretation). Target audience: General audience / everyone at OIST and beyond. Freely accessible to all OIST members and guests without registration (also via Zoom).

TSVP Talk: "Recruiting, Developing, and Retaining Excellent Researchers in the Faculty of Science at the University of Zurich" by Owen Petchey

Seminar, as part of Thematic Program on Response Diversity
Language: English (no interpretation). Target audience: General audience / everyone at OIST and beyond. Freely accessible to all OIST members and guests without registration (also via Zoom).