Modelling and analysis of phase transitions

seminar: A variational approach to the evolution flow associated to the simplest class of polyconvex functionals

speaker: Giuseppe Savaré (Università Bocconi)

abstract: We will present some results (in collaboration with L. Ambrosio and S. Lisini) on the gradient flow associated to polyconvex functionals depending only on the determinant of the gradient of a vector transformation. We will show that the natural variational approximation scheme will converge to the regular solution recently proposed by Evans, Gangbo and Savin, and we will discuss its link with the nonnegative solution of a suitable nonlinear diffusion equation. In particular, in the case of the porous medium equation, we will show that the variational approach overcomes the difficulties arising from the presence of an evolving free boundary.

timetable:
Thu 19 Jan, 15:15 - 16:00, Sala Stemmi
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