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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Plenary Lecture 14: Free boundary problems for mec
hanical models of tumor growth - Vzquez\, JL (Univ
ersidad Autonoma de Madrid)
DTSTART;TZID=Europe/London:20140627T150000
DTEND;TZID=Europe/London:20140627T154500
UID:TALK53197AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/53197
DESCRIPTION:Mathematical models of tumor growth\, now commonly
used\, present several\nlevels of complexity\, bo
th in terms of the biomedical ingredients and the\
nmathematical description. The simplest ones conta
in competition for space\nusing purely fluid mecha
nical concepts. Another possible ingredient is the
\nsupply of nutrients. The models can describe the
tissue either at the level\nof cell densities\, o
r at the scale of the solid tumor\, in this latter
case\nby means of a free boundary problem.\n\nWe
first formulate a free boundary model of Hele-Shaw
type\, a variant\nincluding growth terms\, starti
ng from the description at the cell level and\npas
sing to a certain singular limit which leads to a
Hele-Shaw type problem.\nA detailed mathematical a
nalysis of this purely mechanical model is\nperfor
med. Indeed\, we are able to prove strong converge
nce in passing to the\nlimit\, with various unifor
m gradient estimates\; we also prove uniqueness fo
r\nthe limit problem. At variance with the classic
al Hele-Shaw problem\, here\nthe geometric motion
governed by the pressure is not sufficient to\ncom
pletely describe the dynamics.\n\nUsing this theor
y as a basis\, we go on to consider a more complex
model\nincluding nutrients. Here\, technical dif
ficulties appear\, that reduce the\ngenerality and
detail of the description.\nWe prove uniqueness f
or the system\, a main mathematical difficulty.\n\
nJoint work with Benoit Perthame\, Paris\, and Fe
rnando Quiros\, Madrid\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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