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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
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.AP2024
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…