The total variation, which is used as a regularizer in inverse problems in imaging or to compute minimal surfaces, is the simplest example of a convex functional whose minimizers are typically discontinuous. This raises interesting numerical issues, as there are many ways to discretize it, most of which with drawbacks such as a loss of isotropy or important numerical diffusion. In this talk I will review some recent results (obtained in collaboration with C. Caillaud and T. Pock (TU Graz)) about the discret
Christina Lienstromberg , University of Bonn Analysis of non-Newtonian thin-film equations I will offer an insight into mathematical models describing the dynamic behavior of non-Newtonian thin films. The resulting PDEs are in general nonlinear, degenerate, of fourth order, and with a possibly “ weak ” dependence of the coefficients. I will discuss recent results on such an evolution equation for the interface separating two viscous immiscible fluids, confined between two concentric cylinders rotating at a
Elisabetta Rocca , University of Pavia A phase-field prostate cancer growth with chemotherapy and antiangiogenic therapy effects Here, we present a mathematical model of prostate cancer growth and chemotherapy recently introduced in collaboration with P. Colli, H. Gomez, G. Lorenzo, G. Marinoschi, an A. Reali. We use the phase-field method to describe tumor growth, which we assume to be driven by a generic nutrient following reaction-diffusion dynamics. Cytotoxic chemotherapy is included as a term downregul