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SUMMARY:Plenary Lecture 14: Free boundary problems for mechanical models o
 f tumor growth - Vzquez\, JL (Universidad Autonoma de Madrid)
DTSTART:20140627T140000Z
DTEND:20140627T144500Z
UID:TALK53197@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Mathematical models of tumor growth\, now commonly used\, pres
 ent several\nlevels of complexity\, both in terms of the biomedical ingred
 ients and the\nmathematical description. The simplest ones contain competi
 tion for space\nusing purely fluid mechanical concepts. Another possible i
 ngredient is the\nsupply of nutrients. The models can describe the tissue 
 either at the level\nof cell densities\, or at the scale of the solid tumo
 r\, 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 g
 rowth terms\, starting from the description at the cell level and\npassing
  to a certain singular limit which leads to a Hele-Shaw type problem.\nA d
 etailed mathematical analysis of this purely mechanical model is\nperforme
 d. Indeed\, we are able to prove strong convergence in passing to the\nlim
 it\, with various uniform gradient estimates\; we also prove uniqueness fo
 r\nthe limit problem. At variance with the classical Hele-Shaw problem\, h
 ere\nthe geometric motion governed by the pressure is not sufficient to\nc
 ompletely describe the dynamics.\n\nUsing this theory as a basis\, we go o
 n to consider a more complex model\nincluding nutrients. Here\,  technical
  difficulties appear\, that reduce the\ngenerality and detail of the descr
 iption.\nWe prove uniqueness for the system\, a main mathematical difficul
 ty.\n\nJoint work with Benoit Perthame\, Paris\, and  Fernando Quiros\, Ma
 drid\n
LOCATION:Seminar Room 1\, Newton Institute
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