On the incompressible limit for a tumour growth model incorporating convective effects
Noemi David, Markus Schmidtchen
Abstract
Abstract In 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.
Topics & Concepts
Limit (mathematics)CompressibilityLimitingMathematicsWork (physics)AdvectionConvectionMechanicsBoundary (topology)Mathematical analysisGeometryPhysicsThermodynamicsMechanical engineeringEngineeringMathematical Biology Tumor GrowthNavier-Stokes equation solutionsGeometric Analysis and Curvature Flows