| Credits |
8 credit points |
| Instructors |
Doelman, A. (Universiteit van Amsterdam), Hulshof, J. (Vrije Universiteit) |
| E-mail |
A.Doelman@cwi.nl, J.Hulshof@few.vu.nl |
| Aim |
The aim of this course is to obtain a basic knowledge of the theory of PDEs (elliptic, parabolic and hyperbolic). Participants will be introduced to classical techniques, as well as to Hilbert space methods. Developing practical skills by which PDEs can be studied is a second important aspect of the course. |
| Description |
The first PDEs encountered in this course are - linear and nonlinear - first order equations. The concept of weak solutions - a central topic in the course - is introduced in the context of shock waves. Next, the classical theory of hyperbolic (wave), parabolic (diffusion) and elliptic (Laplace) equations is developed (eigenfunction expansions, functions of Green, maximum principles). A brief introduction to Sobolev spaces and Hilbert space methods accumulates in the proof of the existence of weak solutions of linear elliptic equations by the Lax-Milgram Lemma. Furthermore, eigenvalue problems and expansions of eigenfunctions are studied through these methods. The equations studied in this course in general have N-dimensional spatial variables, although the theory is mostly developed and presented for N=2 or N=3. |
| Examination |
Based on take home exercise series. |
| Literature |
- 'Lectures Notes on Partial Differential Equations' by A. Doelman
- J.C. Robinson: Infinite Dimensional Dynamical Systems. Cambridge U.P.
|
| Prerequisites |
A basic knowledge real and complex analysis and/or calculus. A background in ordinary differential equations and/or dynamical systems. |
