On incompressible limit for some tissue growth models / Solutions to nonlinear Schroedinger-type problems - recent results and future plans

Abstract

(TD): I will discuss some approaches to mathematical modelling of living tissues, with applications to tumour growth. In particular, I will describe recent results related to the incompressible limit of a compressible model which builds a bridge between density-based description and a geometric free-boundary problem by passing to the singular limit in the pressure law. 

(BB): We are interested in existence and multiplicity results to nonlinear Schroedinger-type problems. We will provide a review of recent results concerning local and non-local problems, with presence of bounded and/or singular potentials and different kind of nonlinearities (including sign-changing ones). We will propose abstract settings for unconstrained problems, as well as constrained ones (with prescribed L2-norm of a solution). Finally, we will present research plans for the future, including similar topics and more distant ones.

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Zoom:

https://us02web.zoom.us/j/82881783943?pwd=TUp3OGNvZ3R5akpXclZESmx2aGVkUT09