Event(s) on May 2022

• Wednesday, 11th May, 2022

  Title:	Mathematical Models of Living tissues and Free Boundary Problems
  Speaker:	Prof Benoît Perthame, Sorbonne University, France
  Time/Place:	16:00  -  17:00 Zoom, (Meeting ID: 916 9493 0182)
  Abstract:	Tissue growth, as it occurs during solid tumors, can be described at a number of different scales from the cell to the organ. For a large number of cells, 'fluid mechanical' approaches have been advocated in mathematics, mechanics or biophysics. Since the 70's the mathematical modeling has been progressing regularly, posing new mathematical questions. We will give an overview of the modeling aspects and focuss on the links between two types of mathematical models. The 'compressible' description describes the cell population density using systems of porous medium type equations with reaction terms. A more macroscopic 'incompressible' description is based on a free boundary problem close to the classical Hele-Shaw equation. In the stiff pressure limit, one can derive a weak formulation of the corresponding Hele-Shaw free boundary problem and one can make the connection with its geometric form. The mathematical tools related to these questions include multi-scale analysis, Aronson-Benilan estimate, uniform $L^4$ estimate on the pressure gradient and emergence of instabilities.

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