3 papers
math.AP2026
On a relaxed Cahn-Hilliard tumour growth model with single-well potential and degenerate mobility
Cecilia Cavaterra, Matteo Fornoni, Maurizio Grasselli +1
We consider a phase-field system modelling solid tumour growth. This system consists of a Cahn-Hilliard equation coupled with a nutrient equation. The former is characterised by a…
math.AP2026
Multiscale analysis of a kinetic equation for mechanotaxis
Benoît Perthame, Francesco Salvarani, Shugo Yasuda
We present a new kinetic equation for cell migration driven by mechanical interactions with the substrate, an effect not previously captured in kinetic models, and essential for ex…
math.AP2025
Existence, regularity and stability in a strongly degenerate nonlinear diffusion and haptotaxis model of cancer invasion
Benoit Perthame, Chiara Villa
We consider a mathematical model of cancer cell invasion of the extracellular matrix (ECM), comprising a strongly degenerate parabolic partial differential equation for the cell vo…