PARTIAL DIFFERENTIAL EQUATIONS: FROM MODELLING TO THEORY
PARTIAL DIFFERENTIAL EQUATIONS: FROM MODELLING TO THEORY
| A.Y. | Credits |
|---|---|
| 2021/2022 | 4 |
| Lecturer | Office hours for students | |
|---|---|---|
| Giovanni Molica Bisci |
| Teaching in foreign languages |
|---|
|
Course entirely taught in a foreign language
English
This course is entirely taught in a foreign language and the final exam can be taken in the foreign language. |
Assigned to the Degree Course
| Date | Time | Classroom / Location |
|---|
| Date | Time | Classroom / Location |
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Learning Objectives
Aim of the course is to give to the students some basic tools and topics in partial differential equations.
Program
1. Introduction to Elliptic problems on graphs.
2. Elements of Graph Theory:
2.1 Generalities. Locally finite graphs.
2.2 Sobolev spaces on graphs.
2.3 Embedding results.
3. Variational methods:
3.1 A local minimum result for smooth functionals.
3.2 Multiple critical point results.
3.3 Infinitely many critical points.
4. Applications to the Dirichlet problems on graphs.
Bridging Courses
There are no mandatory prerequisites.
Learning Achievements (Dublin Descriptors)
Knowledge and understanding:
At the end of the course the student will learn the basic notions on PDEs.
Applying knowledge and understanding:
At the end of the course the student will learn the methodologies on PDEs
and will be able to apply them to the study of various problems.
Making judgements:
At the end of the course the student will be able to apply the techniques of PDEs in order to solve new problems, also coming from real-world applications.
Communications skills:
At the end of the course the student will have the ability to express the fundamental notions of
PDEs using a rigorous terminology.
Learning skills:
During the course the student will learn the ability to study the notions of PDEs, also in order to use it in solving different kind of problems.
Teaching Material
The teaching material prepared by the lecturer in addition to recommended textbooks (such as for instance slides, lecture notes, exercises, bibliography) and communications from the lecturer specific to the course can be found inside the Moodle platform › blended.uniurb.it
Teaching, Attendance, Course Books and Assessment
- Teaching
Theorical and practical lessons.
- Attendance
Although strongly recommended, course attendance is not mandatory.
- Course books
G. Molica Bisci - V. Radulescu - R. Servadei, Variational Methods for Nonlocal Fractional Problems, Encyclopedia of Mathematics and its Applications, 162 Cambride University Press - ISBN: 9781107111943. Foreword by J. Mawhin.
G. Molica Bisci - P. Pucci, Nonlinear Problems with Lack of Compactness, De Gruyter Series in Nonlinear Analysis and Applications, 36 (2021).
G. Molica Bisci, Variational and Topological Methods for Nonlocal Fractional Periodic Equations, Recent developments in the Nonlocal Theory, De Gruyter (2018).
- Assessment
The exam of Optimization Methods consists of an oral exam on the topics of the course.
- Disabilità e DSA
Le studentesse e gli studenti che hanno registrato la certificazione di disabilità o la certificazione di DSA presso l'Ufficio Inclusione e diritto allo studio, possono chiedere di utilizzare le mappe concettuali (per parole chiave) durante la prova di esame.
A tal fine, è necessario inviare le mappe, due settimane prima dell’appello di esame, alla o al docente del corso, che ne verificherà la coerenza con le indicazioni delle linee guida di ateneo e potrà chiederne la modifica.
Additional Information for Non-Attending Students
- Teaching
Theorical and practical lessons.
- Attendance
Although strongly recommended, course attendance is not mandatory.
- Course books
G. Molica Bisci - V. Radulescu - R. Servadei, Variational Methods for Nonlocal Fractional Problems, Encyclopedia of Mathematics and its Applications, 162 Cambride University Press - ISBN: 9781107111943. Foreword by J. Mawhin.
G. Molica Bisci - P. Pucci, Nonlinear Problems with Lack of Compactness, De Gruyter Series in Nonlinear Analysis and Applications, 36 (2021).
G. Molica Bisci, Variational and Topological Methods for Nonlocal Fractional Periodic Equations, Recent developments in the Nonlocal Theory, De Gruyter (2018).
- Assessment
The exam of Optimization Methods consists of an oral exam on the topics of the course.
- Disabilità e DSA
Le studentesse e gli studenti che hanno registrato la certificazione di disabilità o la certificazione di DSA presso l'Ufficio Inclusione e diritto allo studio, possono chiedere di utilizzare le mappe concettuali (per parole chiave) durante la prova di esame.
A tal fine, è necessario inviare le mappe, due settimane prima dell’appello di esame, alla o al docente del corso, che ne verificherà la coerenza con le indicazioni delle linee guida di ateneo e potrà chiederne la modifica.
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