BEGIN:VCALENDAR
PRODID:-//ical.php//NONSGML kigkonsult.se iCalcreator 2.8//
VERSION:2.0
METHOD:PUBLISH
X-WR-CALDESC:Montana State University Social Calendar Brief Feed
X-WR-TIMEZONE:America/Denver
BEGIN:VEVENT
UID:20210120T143942CET-31852xta9W@ical.php
DTSTAMP:20210120T130142Z
CLASS:PUBLIC
DESCRIPTION:Starting point will be a quasilinear system of diffusion-reacti
on equations\, one of which (i) degenerates if the dependent variable vani
shes\, and (ii) attains a super-diffusion\nsingularity if the dependent va
riable reaches an a priori known critical value. We introduced this type o
f equations many years ago to model bacterial biofilms. Both effects (i)
and (ii) introduce numerical (and analytical) challenges: (i)\, like the p
orous medium equation\, leads to the formation of sharp interfaces and gra
dient blow-up. (ii) is characterised by blow-up of the density-dependent d
iffusion coefficient\, which prevents the application of standard argumen
ts to show boundedness of solutions.\n\nAfter semi-discretisation in space
one obtains a very stiff system of ordinary differential equations that\,
owing to (ii)\, a priori does not satisfy a Lipschitz condition. We explo
re this system using regularistaion techniques. We are able to prove that
(for practically\nreasonable assumptions on initial and boundary condition
s) the numerical solutions remain bounded by unity (as they ought to) and
that traditional ODE integrators can be safely applied. We present a small
application of this method that is concerned with quorum sensing cross-ta
lk in a biofilm community.\nThis is joint work with Maryam Ghasemi (now at
the University of Waterloo).
DTSTART:20201105T150000
DTEND:20201105T160000
LOCATION:Webex Meeting number: 120 556 7048 Password: applied
SUMMARY:Integration of a degenerate diffusion-reaction system with an appli
cation to cross-talk in biofilms
END:VEVENT
END:VCALENDAR