# Functional Analysis

## Nonlinear PDEs II

Summer 2013

### Lectures

Mondays and Thursdays 10-12, SR 1.008

Prof.dr. J. J. L. Velázquez

### Classes

Wednesday 14-16, room N 0.007

M. Zaal

### Office hours

By appointment.

### Literature

- L. C. Evans. Partial Differential Equations. Graduate Studies in Mathematics vol. 19, American Mathematical Society, 1991.
- D. Henry. Geometric theory of seminlinear parabolic equations. Lecture Notes in Mathematics vol. 840, Springer-Verlag, 1981.
- J. Smoller. Shock Waves and Reaction-Diffusion Equations. Grundlehren der mathematischen Wissenschaften vol. 258, Springer-Verlag, 1982.
- G. B. Whitham. Linear and Nonlinear Waves. John Wiley & Sons, 1974.

### Examination

There will be an oral examination at the end of the course. To sit the exam, students have to gain at least 50% of the overall marks of the problem sheets as requirement for passing the classes.

The first opportunity to sit the exam has passed. The second opportunity will be on September 19th and 20th.

### Problem sheets

- Sheet 1, due 24.04.2013
- Sheet 2, due 02.05.2013 in lecture
- Sheet 3, due 08.05.2013
- Sheet 4, due 15.05.2013
- Sheet 5, due 27.05.2013 in lecture
- Sheet 6, due 05.06.2013
- Sheet 7, due 19.06.2013

Alternate solution to Problem 2 - Sheet 8, due 26.06.2013

NOTE: Ex. 3, part 3 contains a mistake: the initial condition for v should be 2 for x>0 (and 0 for x<0). For this reason, solving (2) and part 4 of the exercise are optional. - Sheet 9, due 03.07.2013

construction of a solution from elementary waves - Sheet 10, optional, please hand in for correction 10.07.2013