Affiliation:
1. Institut Camille Jordan Université Claude Bernard Lyon 1 43 BD DU 11 Novembre 1918 Villeurbanne Cedex 69622 France
2. Faculty of Mathematics Willers‐Bau, Technische Universität Dresden Dresden Germany
Abstract
AbstractIn this work we study a tissue growth model with applications to tumour growth. The model is based on that of Perthame, Quirós, and Vázquez proposed in 2014 but incorporates the advective effects caused, for instance, by the presence of nutrients, oxygen, or, possibly, as a result of self‐propulsion. The main result of this work is the incompressible limit of this model which builds a bridge between the density‐based model and a geometry free‐boundary problem by passing to a singular limit in the pressure law. The limiting objects are then proven to be unique.
Subject
Applied Mathematics,General Mathematics
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