Dobbelt gæsteforedrag: Poul G. Hjorth, DTU og Anton Evgrafov, AAU


03.12.2021 kl. 13.00 - 15.15


kl 13:00 - 14:00 Poul G. Hjorth (DTU)

Titel: Anvendt anvendt matematik - om industriarbejdsgrupperne ESGI

ESGI = European Study Groups with Industry er én af mange samarbejdsformer mellem virksomheder og universiteter omkring matematisk modellering af industrielle problemstillinger eller processer. Der er tale om intense arbejdsmøder af en uges varighed hvor matematikere i grupper forsøger at udrede matematiske spørgsmål stillet af deltagende virksomheder. I Danmark har vi afholdt denne type møder i mere end 20 år; jeg vil skitsere baggrunden og give nogle eksempler på den type af opgaver der har været behandlet gennem årene.

Kl. 14:00 - 14:15 Kaffe og kage

Kl. 14:15 - 15:15 Anton Evgrafov (AAU)

Title: A tale of two-point fluxes

Recently there has been a tremendous increase in research interest in nonlocal equations.  To a large extent, this trend is driven by applications.  For example, in continuum mechanics the utilization of nonlocal, derivative-free models offers an exciting possibility for a unified framework allowing for such singular phenomena as crack propagation and cavitation.  In several other disciplines, apparent nonlocal interactions between constitutive particles are an inherent part of the model, which often becomes evident owing to the continuing miniaturization of such systems.  Finally, the time is ripe for developing such models, as our mathematical understanding of nonlocality has matured significantly since the seminal nonlocal characterization of Sobolev spaces by Bourgain, Brezis and Mironescu.

We will outline the nonlocal paradigm using the example of a peridynamic model of a steady state, nonlocal, linear scalar diffusion.  We will then focus on the dual variational principle for such equations, which is expressed using the nonlocal two-point flux as the primary unknown quantity.  We will discuss the existence of solutions to the nonlocal equations and the associated control in the coefficients problems, and Gamma-convergence towards the local, PDE-based model as the nonlocal interaction horizon shrinks to zero.  We will try to emphasize both the similarities and the striking differences between the local and nonlocal models.

This talk is based on a joint work with Jose C. Bellido from the University of Castilla-La Mancha.


Department of Mathematical Sciences


Skjernvej 4A, AUD B - 5.034