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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…
On the determination of ischemic regions in the monodomain model of cardiac electrophysiology from boundary measurements
Elena Beretta, Cecilia Cavaterra, Luca Ratti
In this paper we consider the monodomain model of cardiac electrophysiology. After an analysis of the well-posedness of the model, we determine an asymptotic expansion of the pertu…
Pointwise gradient bounds for entire solutions of elliptic equations with non-standard growth conditions and general nonlinearities
Cecilia Cavaterra, Serena Dipierro, Alberto Farina +2
We give pointwise gradient bounds for solutions of (possibly non-uniformly) elliptic partial differential equations in the entire Euclidean space. The operator taken into account i…
A nonlinear model for marble sulphation including surface rugosity: theoretical and numerical results
Elena Bonetti, Cecilia Cavaterra, Francesco Freddi +2
We consider an evolution system describing the phenomenon of marble sulphation of a monument, accounting of the surface rugosity. We first prove a local in time well posedness resu…