Abstract: We are interested in the motion of interfaces driven by forced mean curvature flow through a field of random obstacles. The effective large scale behavior is expected to be a first order motion. However, previous results required a lower positive bound on the combined forcing, translating to a global minimum speed for the interface and hence the absence of any actual obstacles.
We obtain a quantitative homogenization result in two dimensions even with locally negative forcing and thus potentially allowing pinned interfaces and eventually enclosures left behind the main front. The positivity of the combined forcing is replaced with the assumption, that - for a range of small thin boxes - the interface percolates from bottom to top at some minimum speed with high enough probability. (Joint work with Julian Fischer)
Quantitative Homogenization of Forced Mean Curvature Flow through a random field of obstacles
06.11.2024 15:00 - 15:30
Organiser:
SFB 65
Location:
TU Wien, Wiedner Hauptstraße 8, 1040 Vienna, green area, second floor, seminar room DA 02 A; and Zoom
Related Files
- pde_afternoon_2024-11-06.pdf 922 KB