Qualitative Theory of Partial Differential Equations (MAE815)
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General
| School |
School of Science |
|---|---|
| Academic Unit |
Department of Mathematics |
| Level of Studies |
Undergraduate |
| Course Code |
MAE815 |
| Semester |
7 |
| Course Title |
Qualitative Theory of Partial Differential Equations |
| Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
| Course Type |
Special Background |
| Prerequisite Courses | - |
| Language of Instruction and Examinations |
Greek, English |
| Is the Course Offered to Erasmus Students |
Yes (in English) |
| Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
| Learning outcomes |
The course introduces the students to more advanced topics of the Theory of Partial Differential Equations, like the necessity for studying weak solutions, especially in nonlinear problems, and the development of a theory for the existence, uniqueness and regularity of solutions for general classes of data (coefficients, domain of existence of solutions, boundary/initial values etc.) when the determination of an explicit representation of the solutions is generically not possible. It is stressed that the understanding of the behavior of the solutions of a PDE is not determined primarily by the determination of a representation but by the derivation of the properties of the solution from the structure of the equation. |
|---|---|
| General Competences |
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Syllabus
In the course it is possible to choose among several topics. Indicatively and not exclusively we mention: Introduction to Hamilton-Jacobi equations and conservation laws. Weak solutions. Burgers equation, shock waves. Introduction to the theory of weak solutions in Sobolev spaces (or to the Schauder theory of classical solutions in Hoelder spaces) of the Dirichlet boundary value problem for linear second order uniformly elliptic equations in smooth bounded domains of n-dimensional Euclidean space.
Teaching and Learning Methods - Evaluation
| Delivery |
Classroom (face-to-face) | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Use of Information and Communications Technology |
The students may contact the lecturer by e-mail | ||||||||||
| Teaching Methods |
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| Student Performance Evaluation |
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Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Γ. Δ. Ακρίβης, Ν. Δ. Αλικάκος. Μερικές Διαφορικές Εξισώσεις. 2η έκδοση. Σύγχρονη Εκδοτική, 2017.
- L. C. Evans. Partial Differential Equations. Second edition. AMS, 2010.
- G. B. Folland. Introduction to Partial Differential Equations. Princeton University Press, 1995.
- D. Gilbarg, N. S. Trudinger. Elliptic Partial Differential Equations of Second Order. Springer, 2001.