PDE seminar, April 22th 2015
Wednesday 22th EHESS, 190-198 Avenue de France, room 466, 4th floor - 75013 Paris
Mathematical study of a cell model for tumor growth : travelling front and incompressible limit
We consider mathematical models at macroscopic scale to describe tumor growth. In this view, tumor cells are considered as an elastic material subjected to mechanical pressure. Two main classes of model can be encountered: those describing the dynamics of tumor cells density and those describing the dynamic of the tumor thanks to the motion of its domain. These latter models are free boundary problem. We will show that such free boundary problem of Hele-Shaw type can be derived thanks to an incompressible limit from models describing the dynamics of cells density.
Moreover, for this model we study the existence of travelling waves, allowing to describe the spread of the tumor.
Poster here
We consider mathematical models at macroscopic scale to describe tumor growth. In this view, tumor cells are considered as an elastic material subjected to mechanical pressure. Two main classes of model can be encountered: those describing the dynamics of tumor cells density and those describing the dynamic of the tumor thanks to the motion of its domain. These latter models are free boundary problem. We will show that such free boundary problem of Hele-Shaw type can be derived thanks to an incompressible limit from models describing the dynamics of cells density.
Moreover, for this model we study the existence of travelling waves, allowing to describe the spread of the tumor.
Poster here
Propagation in models of kinetic type from biology
In this talk, we will be interested in biological invasions for which the (macroscopic) spatial movement is highly influenced by a microscopic structure of the populations. From experiments, one can see that this happens for collective motion of bacteria and dispersal evolution in e.g. cane toads populations. Models of kinetic type are thus needed to describe accurately such kind of invasions. I will present some results concerning the study of propagation in two types of models. First, kinetic reaction-transport equations, inspired by bacterial dispersal. Second, reaction-diffusion-mutation equations, modeling dispersal evolution. We will discuss two points of view : the (non-)existence of travelling waves, and geometric optics. |