Lecture Course : 250088 VU
April  11 - 25, 2024
Time: 11:00 - 13:00\13:15
Start: April 11, 2024
Further dates: Friday, April 12, 2024, Tuesday, April 16, 2024, Wednesday April 17, 2024 (11:00 - 13:15)
End: Thursday, April 25, 2024 (11:00 - 13:15)
 

Abstract:
In this series of lectures, using the notion of Γ-convergence as introduced by De Giorgi in 1975 (see [27]), we derive the variational model for phase tran- sitions between two fluids as an asymptotic limit of a family of Cahn-Hilliard energies (also known as the Modica-Mortola functional, in the mathemat- ical community). We will then consider a variational model for the in- teraction between homogenization and phase separation when small scale heterogeneities are present in the fluids.

Aim, contents and method of the course:
The course is intended to provide an invitation to some actual research directions in the calculus of variations, especially in relation with materials science. Variational models and methods for the description of phase change, homogenization, and high-contrast materials will be presented. Variational approximation by Gamma-convergence will be the overarching technical setting.

Reading list:
The course will be based on scientific papers, which will be provided at the beginning of the course.
As general reference on the subject one can indicate the classical monographs:

1) Dal Maso, Gianni. An introduction to Γ-convergence. (English summary)
Progress in Nonlinear Differential Equations and their Applications, 8. Birkhäuser Boston, Inc., Boston, MA, 1993.
2) Dacorogna, Bernard. Introduction to the calculus of variations. Third edition. Imperial College Press, London, 2015.
3) Fonseca, Irene; Leoni, Giovanni Modern methods in the calculus of variations: Lp spaces. Springer Monographs in Mathematics. Springer, New York, 2007.

Lecture Course Announcement (pdf)

Link to the course directory