6 papers
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…
Carleman estimates for backward Cahn-Hilliard-reaction-diffusion problems
Abramo Agosti, Elena Beretta, Cecilia Cavaterra +2
We study a backward inverse problem for a coupled Cahn-Hilliard-reaction-diffusion system. Our main result is a Carleman estimate for a fourth-order/second-order parabolic system w…
Optimal control of the fidelity coefficient in a Cahn-Hilliard image inpainting model
Elena Beretta, Cecilia Cavaterra, Matteo Fornoni +1
We consider an inpainting model proposed by A. Bertozzi et al., which is based on a Cahn-Hilliard-type equation. This equation describes the evolution of an order parameter that re…
Identifying early tumour states in a Cahn-Hilliard-reaction-diffusion model
Abramo Agosti, Elena Beretta, Cecilia Cavaterra +2
In this paper, we tackle the problem of reconstructing earlier tumour configurations starting from a single spatial measurement at a later time. We describe the tumour evolution th…
Iterative algorithms for the reconstruction of early states of prostate cancer growth
Elena Beretta, Cecilia Cavaterra, Matteo Fornoni +2
The development of mathematical models of cancer informed by time-resolved measurements has enabled personalised predictions of tumour growth and treatment response. However, frequ…
Mathematical analysis of a model-constrained inverse problem for the reconstruction of early states of prostate cancer growth
Elena Beretta, Cecilia Cavaterra, Matteo Fornoni +2
The availability of cancer measurements over time enables the personalised assessment of tumour growth and therapeutic response dynamics. However, many tumours are treated after di…