- Docente: Ermanno Lanconelli
- Credits: 6
- SSD: MAT/05
- Language: Italian
- Moduli: Ermanno Lanconelli (Modulo 1) Giovanni Cupini (Modulo 2)
- Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2)
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Mathematics (cod. 8208)
Learning outcomes
At the end of the course the student knows basic notions from
the theory od Elliptic, Parabolic and Hyperbolic Partial
Differentia Equations. He is able to study and
understand elementary
differential models in applied sciences. He is also able to
face high level topics from the general
theory of Partial Dirrential Equations.
Course contents
Linear second order partial differential operators with non-negative characteristic form: Picone's maximum principle, strong maximum principle, maxima propagation.
The Perron method for the heat equation. Cauchy problem for the heat equation: existence theorems and uniqueness theorems. Liouville type theorems.
Introduction to the diffusion operators of Kolmogorov-Fokker-Planck type.
Readings/Bibliography
Afternotes of the lectures.
Teaching methods
The course consists of lessons describing the fundamental concepts of the program. Lessons are completed with examples illuminating the theoretical content. Futhermore exercises are solved in the classroom.
Assessment methods
1) Homework: solution of some problems form a list given by the
lecturer.
2) Oral exams on some arguments, chosen by the student, from the
main
chapters of the course.
Office hours
See the website of Ermanno Lanconelli
See the website of Giovanni Cupini